It was cold, wet and horrible – the kind of night to make a continental manager pine for those winter breaks. There have been plenty of pictures doing the rounds in recent days of European players reclining on beach loungers in expensive-looking locations. Pep Guardiola’s pleasure was a first taste of football’s oldest competition.

It all turned out rather nicely. The spotlight had burned intensely on the Manchester City manager, a result of a few sketchy results in December and his tetchiness after his team’s home win over Burnley last Monday. He had given the impression of being a little embattled with this English football lark. The vultures were circling.

His City team gave a powerhouse performance, shaped by a virtuoso display from David Silva, the floating midfield sprite, and marked by ruthlessness. It was an occasion when everything went right for Guardiola’s team. Take the fourth goal. Yaya Touré sliced his shot following Raheem Sterling’s pass back to him but it flew perfectly into Sergio Agüero’s space and he touched home deftly.

The game had turned on a soft 33rd-minute penalty, awarded after Pablo Zabaleta drew contact from Angelo Ogbonna. Touré rifled it past Adrián. But City had been the better team up until that point and they cut loose thereafter.

Sterling pressured Havard Nordtveit into putting through his own goal and Silva ended the game as a contest with the third before half-time. He practically had a cigar out before he placed his shot past Adrián.

Slaven Bilic was still smouldering after West Ham’s 2-0 loss to Manchester United here on Monday, when Sofiane Feghouli had been wrongly sent off in the 15th minute. The card would be rescinded but it was too little, too late. “I still feel angry and disappointed,” Bilic said, earlier on Friday.

He could express his exasperation over the penalty award but this was a night when West Ham were outclassed by a strong Guardiola selection.

Bilic used Dimitri Payet only as a 57th-minute substitute and the winger managed to nutmeg Agüero. There was precious little else for West Ham to remember. Feghouli blew their only clear chance at 1-0 down and it was a terrible miss from close range.

Guardiola’s lineups are routinely difficult to classify, such is the movement of his players and the manner in which they interchange positions, and nobody is harder to pin down than Silva. His licence to roam was pronounced and so, too, was his threat.

There was one lovely cutback in the early running for Zabaleta, who offered a passable impression of a box-to-box midfielder, and his shot was blocked by Winston Reid while, from a Gaël Clichy pass, Silva worked Adrián.

Watching football in this vast bowl remains a curious experience. There were moments here when the noise levels rose sharply but many more when it all seemed to drift away on the breeze. Perhaps City simply succeeded in taking the sting out of the occasion.

Their passing was too slick for West Ham and it felt symbolic that Bilic’s team did not even pick up a yellow card in what was a humiliation. They could not get close to their City counterparts.

The visitors had further advertised the opening goal through Sterling and Agüero. The first chance was created by Silva only for Sterling to choose the wrong option in jinking inside Nordtveit; Reid nipped back to tackle. Agüero’s effort was a beautifully sculpted side-on volley, after Michail Antonio’s ropey clearance. Adrián tipped over.

It took the penalty to break the deadlock and it was a depressing moment for West Ham and Ogbonna. Everybody inside the stadium knew that Zabaleta was going to take a touch following Silva’s cute pass and then see if there was any contact to be had inside the area. Thanks to Ogbonna, there was. Did Zabaleta initiate it? Possibly. Yet it was there and the referee, Michael Oliver, was entitled to point to the spot. From West Ham’s point of view, it just felt so needless.

West Ham’s big moment came immediately after the penalty. Antonio bustled through and his shot was pushed out by Willy Caballero but only as far as Feghouli. He looked odds-on to score but when Clichy dived into a saving challenge, he managed to distract him and Feghouli shot badly wide. Antonio had also worked Caballero on 14 minutes.

City summoned a devastating one-two punch. First, Bacary Sagna ran on to Agüero’s ball forward and put a devilish delivery into the area towards Sterling. In front of his own goal, Nordtveit was in that unenviable position for a defender. He could not leave it; he had to do something. The right-back stretched out his right leg but he succeeded only in diverting it past Adrián.

Minutes later, it was 3-0. Sterling swapped passes with Agüero and bombed away and, when he looked across, he had Silva completely unmarked in the centre. Silva had the time and composure to take a touch following Sterling’s low cross and, with Adrián grounded, impudently rolled the ball past him.

Guardiola could afford to remove Silva on 57 minutes, and Kevin De Bruyne and Touré after that, and the last word went to John Stones. From the substitute Nolito’s corner, he flashed home a header that the goalline technology showed had crossed the line before Mark Noble’s attempted clearance. It was Stones’s first goal for City since joining last summer.