* “If you want to see Liverpool more successful than in the past, than in the last 24 years, you can do your small part, of course,” said Jurgen Klopp on his Liverpool unveiling. “If you want to make me like Jesus and the next day say, ‘He can’t walk on water’, then we have a problem. I dive.”

Klopp was aiming to tone down expectation and postpone impatience but, on the evidence of the first half-hour at the Etihad, it has taken him six weeks to perform near miracles. This was a team playing at the very peak of its powers, making expensive opponents look like sloppy amateurs. Liverpool scored three times in 32 minutes, and could have had two more still. Their players buzzed around Manchester City’s penalty area like joyful bees enjoying the first warm day of spring.

Klopp has not completed the mission, far from it. But in this 32-minute spell of wonder he offered enough evidence that he was the right choice at the right time. It was stunning to watch, intoxicating for the near-neutral. For a second, you really believed that Liverpool were back.

* Brendan Rodgers was a man who believed in possession as the means to victory. “When you’ve got the ball 65, 70 percent of the time it’s a football death for the other team,” he famously said. “We’re not at that stage yet, but that’s what we’ll get to, it’s death by football.” It became his own managerial suicide note.

Klopp’s own strategy could not be more different. “Now we cannot talk about football philosophy and ball possession, playing like Barcelona, playing like whoever. No. This team needs to create their own style,” he said shortly after arriving in Liverpool. “If you have the ball you have to be creative, but you have to be prepared that if you lose the ball the counter-pressing is very important.”

In the first half, Liverpool registered just 37.4% possession, and completed 129 fewer passes than Manchester City. They also registered six shots, four of them on target. Where Rodgers believed in quantity of possession, Klopp’s Liverpool are focused on quality. It shows.

It is reminiscent of a quote from Chile coach Jorge Sampaoli, made after his side lost to Uruguay with 73% possession last weekend.

“One night, I went to a bar, I was with a woman,” Sampaoli said. “We talked all night. We laughed, we flirted, I paid for several drinks of hers. At around 5am, a guy came in, grabbed her by the arm and took her to the bathroom. He made love to her and she left with him. That doesn’t matter, because I had most of the possession on that night.”

Well, quite.

* Could there be two more different personalities in football management than Manuel Pellegrini and Klopp? One is the relaxed, mild-mannered grandfather who relishes a glass of merlot and some Debussy on the radio. The other is the brash, jokey uncle who wants to take you to Laserquest and playfully punches you that little bit too hard.

Their pre-match interviews epitomised their vast differences. When asked to describe the thinking behind his team selection, Pellegrini went for parodical tedium: “I have picked the best team that I thought would win the game.” Fair.

Klopp, meanwhile, offered a typical japey, close-to-banter-but-not-quite-banter interview. “Hey, that’s football, cool hey? Ha ha ha,” was the sign-off line. There are merits to both styles, providing extra intrigue to matches between them. Laserquest 4-1 Debussy.

* Of course it is necessary to mention just how bad City defended while Liverpool flourished. This was the 15th Premier League or Champions League match that Eliaquim Mangala and Martin Demichelis have started together. Before Saturday evening, City’s record in those games read: Won 12, Drew 2, Lost 0. That has been blown out of the water.

It was the decision to leave Nicolas Otamendi on the bench that made the least sense, even with Juventus to come in midweek. Vincent Kompany’s absence this season has caused City issues – as the below statistic indicates – so why add to this problem?

Man City PL goals conceded this season with Kompany on pitch (720 mins): 1. Man City PL goals conceded, Kompany NOT on pitch (405 mins): 11. — sportingintelligence (@sportingintel) November 21, 2015

Using the pace of Mangala was logical, but having the dancing feet of Coutinho, Firmino and Adam Lallana running around Demichelis became embarrassing during the first period. It was like watching an old dog get worn out just by watching a new litter of puppies at play.

* That was not Pellegrini’s only odd selection decision. Against Manchester United and Sevilla last month, the combination of Fernandinho and Fernando behind Yaya Toure worked brilliantly. Having two bodies protecting the defence gave Toure licence to roam forward without having to constantly be aware of his defensive responsibilities.

The performance against Sevilla was sensational, Pellegrini finally finding a different way to play as City dominated on the counter-attack. Quite why the Chilean chose to abandon that strategy against Liverpool only he knows, but it backfired spectacularly. Fernando was overwhelmed in front of the defence, having to put out multiple fires with one hose.

* The first goal was a result of abysmal defending on City’s part. Bacary Sagna has been excellent this season, but was robbed in his own half by Coutinho. One Brazilian passed to another, and within five seconds Firmino had crossed into the box. Mangala offered a fine impression of Djimi Traore’s own goal against Burnley for Liverpool in 2005.

Liverpool played their own role in the goal, however. The term Gegenpressing was used continuously during Klopp’s early days at Anfield, but this was real evidence for the manager’s effect on the team:

1) Press high up the pitch on the opposition defenders, forcing a mistake.

2) As soon as the ball is won, have players overlapping to create space and cause panic.

3) Hope that panic ends in mistakes.

Pressing in excelsis.

* “There’s a certain amount of poignancy in this, two French players making mistakes,” said Martin Tyler after the first goal, referring to Sagna and Mangala’s errors.

Am I the only one that feels really uncomfortable hearing human tragedy and acts of terrorism contextualised in this way?

* ‘Edwards encourages staff to use his nickname ‘Eddie’, giving a matey feel to the working environment. It is understood Rodgers has another name for him,’ wrote Neil Ashton during his scathing attack on Liverpool’s use of statistics as part of their decision-making in the transfer market. He wasn’t finished there.

‘Edwards fell perfectly into place with FSG’s Moneyball strategy, the statistical model designed to extract maximum value in the transfer market. Clearly, with the club 10th in the league and paying up to three times the going rate for players, it needs refinement.

‘The committee have yet to explain how they came up with the figure of £29million to sign Brazilian forward Roberto Firmino from Hoffenheim, who finished eighth in the Bundesliga last season.’

Shall we talk about Roberto Firmino next then?

The Brazilian was exceptional against City. Klopp’s decision to leave Christian Benteke on the bench was a gamble, but Firmino excelled in a false nine role. He had more shots than any other player on the pitch, and double the number of shots on target. He also played a sublime pass for Coutinho’s goal and won possession eight times. It is this determination that caused Klopp to put faith in him.

As with Memphis Depay at Manchester United, perhaps it’s time to realise just how hard it can be for young players settling in new countries. Given time and support, both are plenty good enough to flourish. And that’s why the committee ‘came up with the figure of £29million’.

* We need clarification on the amount of time afforded within the advantage rule. There was an incident in the second half where Sergio Aguero fouled Milner, with referee Jonathan Moss allowing play to continue when the ball ran to Lallana.

Lallana was given the time to control the ball, dribble forward and then attempt a poor pass which went to a City player. Five or six seconds had passed since the original incident. As ever, it’s the ‘C’ word we’re discussing; where’s the consistency?

* Isn’t it wonderful to see Aguero back? The Argentinean was clearly far from fully fit, but that only meant the moments of brilliance would be less frequent. We still got one.

As if to follow the tone of the match, City’s hope-giving goal came as a result of defensive mishap. Martin Skrtel’s clearance was poor and easily intercepted, Aguero received the ball 30 yards from goal and, well… did what Aguero does.

One of the (many) joys of watching Aguero is his ability to generate power without noticeably trying to hit the ball too hard. That enables him to add curl to his shots, regularly starting the ball outside of the far post and nestling it into the corner. He also evaded Lucas with embarrassing ease. Welcome back, you lovely boy.

* In the 16 Conclusions after Klopp’s first match, I wondered whether there was a risk of Coutinho being turned into an effective worker, thus removing some of his creativity. The early signs are that I was wrong to be concerned, but Klopp deserves credit here too.

With Benteke in the team the pressure was on Coutinho to do most of the creative work, but using both of his Brazilians together means that workload is shared. Firmino and Coutinho were excellent in tandem against Chelsea last month. They stepped things up another notch at the Etihad.

Dovetailing together, the two Brazilians look sublime, an obvious understanding already built up between them. Coutinho has eight league goals and assists in 999 minutes this season. Half of those have come in the 259 minutes when Firmino has also been on the field.

Firmino himself now has three goals and assists in the Premier League. His two assists have been for Coutinho goals, and his goal came from a Coutinho assist. It’s like a Brazilian symbiosis. Sambaosis?

Hard not to feel that the man really responsible for Liverpool's performance today was Dunga, dropping Firmino and Coutinho. — Jonathan Wilson (@jonawils) November 21, 2015

The only black mark in Liverpool’s book came with Coutinho limping off through injury. The Brazilian was smiling as he walked onto the pitch after the final whistle, and Klopp will hope that it is a tweak rather than pull. It would be an immense shame if such progress was stopped in its tracks.

* Although City were outclassed, two of Pellegrini’s players still deserve praise. The first is Kevin de Bruyne, who continues to impress during his early months back in England.

The Belgian completed 49 passes in Liverpool’s half, nine more than any of his team-mates and 26 more than the subdued Raheem Sterling. He also created four chances, only one fewer than the rest of City’s team combined. If City are to win the title, you suspect De Bruyne will be the key component.

* The other is Joe Hart, who made magnificent saves from Firmino and Benteke to stop things becoming more embarrassing still for Pellegrini.

If there was a moment to epitomise the match, it came when Martin Skrtel had expertly given Liverpool a 4-1 lead. “F**K’S SAKE” came the shout from Hart, audible to those watching on television. Indeed, Joe. Nobody saw this coming.

* A word too for James Milner, who will be happier than most with the victory back on old stamping grounds. This week’s England Ladder expressed its doubts about Milner’s continued importance to Roy Hodgson, but this was a strong rebuttal from the defence counsel.

Speaking after the game, Klopp said it was Liverpool’s “passion” that pleased him more than any other part of their display. It is Milner who personifies that characteristic most. He made seven tackles, two more than any other player, and also covered the most distance. Plus ca change.

There is no doubt that some of Milner’s creativity has been starved at Liverpool. Nine of his team-mates created a chance against City , but he was not one of them. Yet with Adam Lallana, Firmino and Coutinho ahead of him, that doesn’t have to be Milner’s remit.

Rodgers once infamously remarked that you “you can live without water for many days”. Milner’s the man faithfully carrying it for when you do need a drink.

* City will be down, but clearly not out in this bonkers Premier League season. Yet there should be more questions raised about Pellegrini’s big-game tactics. In 2015, City have lost to Liverpool (twice), Barcelona (twice), Manchester United, Tottenham, Juventus and Arsenal. August’s 3-0 win over Chelsea is the only victory against a top (top, top?) side. Even that has been put into context by Chelsea’s subsequent results.

The accusation is that City’s manager is leaving them too open, assuming his team’s attack can blow teams away. In those eight defeats, City have conceded 21 goals at a rate of 2.6 per match. That’s not the form of champions, domestically or in Europe. Naivety is an unwelcome trait to find in a 62-year-old manager.

* “Remember to update the Leicester report if they are no longer top after the City game finishes,” reminded Sarah Winterburn as she left the office. It didn’t need changing, of course. This Premier League season continues to be utterly captivating through its own lunacy.

With this victory Liverpool are now eight points from top spot. The realistic hope is to push on for a top-four place, but this is the wrong season to place any glass ceilings on your expectations. Leicester are proof that anyone really can beat anyone. Should Liverpool replicate this performance level on a regular basis, only the sky is the limit.

Daniel Storey