The manager's meticulous methods have allowed the team to flourish and, as Rodgers' former club Swansea prepare to visit Anfield, the supporters have shown their appreciation

They had applauded Brendan Rodgers at Anfield before but never with the universal, unreserved acclaim of the 44th minute of Liverpool's last home game, the 5-1 skewering of Arsenal that amounted to a reprieve for the then Premier League leaders. There was a standing ovation for a ruthless exhibition from Liverpool – a genuine throwback for Anfield elders – and principally for the architect. It was open acceptance of a Liverpool manager who has had to earn every ounce. As Rodgers said afterwards: "I know it has been difficult for the fans. I've got no history or background. They can only see the work on the field. Hopefully they see now that we are all fighting, hungry and have the appetite to make Liverpool great again." A club divided not long ago is united on that score.

Kenny Dalglish had helped heal a fractious period in Liverpool's history but there was still uncertainty and concern over the club's direction under the Fenway Sports Group when Rodgers replaced the Scot as manager on 1 June 2012. "We do not expect miracles overnight nor should anyone else," the principal owner, John W Henry, cautioned that day.

No miracles have revealed themselves yet and a club that measure themselves by silverware was left simmering when Arsenal avenged their league mauling in the FA Cup last Sunday. But even in defeat at the Emirates Liverpool served notice of the remarkable progress made by Rodgers in 21 months. "I spoke to Arsène [Wenger] after the game," said the manager from County Antrim, "and he and his staff said we were the most dangerous attacking team they had played all season."

On Sunday, Liverpool can cut the gap to the leaders, Chelsea, back to four points with victory over their manager's former club Swansea City at Anfield, where 11 wins from 13 league games would equal the return of Dalglish's title-winning team in 1987-88. Rodgers has repeatedly played down Liverpool's title prospects while their form, arithmetic and remaining 12-game schedule suggest a Premier League miracle is achievable. Not that he minds the contradiction.

The priority – the necessity – for this campaign is Champions League qualification after a four-year absence and at the start of the season many outside Anfield regarded that beyond Liverpool. To be managing title talk at this stage is a further illustration of how rapidly Rodgers' methods have taken root.

The Liverpool manager conducts every training session at Melwood, each one prepared in meticulous detail, devised as part of a four-day programme that builds towards a game and with as much emphasis on what the team does without the ball as in possession. "Everyone knows their function in the team," Rodgers says. "We have good organisation and, if you do it day in, day out, you build that momentum."

Thorough preparation is to be expected of a manager who presented his prospective employer with a 180-page dossier, compiled over a 15-year coaching career, when interviewed for the Liverpool job. The document detailed everything from the tactical requirements Rodgers wanted in a player, their personality traits, the need to develop young talent and to play attractive, attacking football that would eventually restore Liverpool's place among the elite. But Rodgers' blueprint for success is not the sign of an inflexible manager. Quite the opposite.

One of his strengths has been a willingness to adapt and offer second chances. There is no great moral dilemma over restoring to the fold a player of Luis Suárez's phenomenal talent, even after the striker was ordered to train away from the first team having accused Rodgers of breaking promises over his future when seeking a transfer to Arsenal. Jordan Henderson, Martin Skrtel and Jon Flanagan, however, have all had doubt over their Anfield careers at some point under Rodgers yet seized their opportunities to become integral to the pursuit of Champions League qualification.

Liverpool's style of play has also been tailored to suit the occasion and the players at the manager's disposal. On his arrival Rodgers spoke of making an afternoon at Anfield the longest 90 minutes of an opponent's life as they chased and harried a Liverpool team dominant in possession.

The recent Anfield blitzes of Everton and Arsenal, by contrast, demonstrated their prowess on the counterattack and at set pieces and the manager's astute tactical tweaks that can devastate the opposition – Daniel Sturridge on the left against the inexperienced John Stones in the Merseyside derby, say, and Suárez on the right against Arsenal's Nacho Monreal. Shifting Steven Gerrard into a holding midfield role at 33 may have been a natural step but it needed Rodgers to readjust an imbalanced side against Aston Villa and then accommodate Philippe Coutinho centrally for the move to work so effectively, so quickly.

Rodgers' experience as a youth-team coach at Reading and Chelsea is evident in the time he spends with players on an individual basis and the pride he takes in their tactical, physical and mental development. "There has been constant improvement in that," he says. "That is what we are paid to do." That influence extends to the Liverpool youth academy where, despite increased production in recent seasons, the director, Frank McParland, and the head of coaching, Rodolfo Borrell, were sacked in November.

Aside from their departures and a biting moment of madness from Suárez, Rodgers' reign has been comparatively free of the controversy, conflict and infighting of several predecessors. Liverpool are in a happier place off the pitch as well as on even though the "transfer committee", of which the manager is part, has enjoyed limited success.

Rodgers' biggest challenge when he arrived at Liverpool was expectation. He explains: "The expectancy here was obviously huge. The success of the club and its great history will always determine that it needs to be up at the top but where the club was at and where it wanted to be were two completely different things. That was the first thing I recognised in the first 50 days here.

"Then it was about slowly creating an environment to learn and improve. Once you have got more time to implement your ideas and everyone understands them, it is a smoother place for you to work. That early period was very, very difficult but I always felt that, even in those tough times, I had seen enough to show that we were progressing.

"We have got a clear vision of what we want to achieve. It is up to the manager to give the confidence to the players and staff that we are going in the right direction. Eventually there comes a point where the players will say: 'I'll go with you,' or: 'I won't.'

"I think we have had enough good performances and results consistently for the players to feel we are going in the right direction. It has been continual work, a lot of hard work, and hopefully the supporters can see that."

They rose to their feet to acclaim it last time out at Anfield.