Philippe Coutinho had not recovered from the pain of missing out on a World Cup in Brazil when the new Premier League season opened in August. Having been overlooked by Luiz Felipe Scolari for a squad that included Fred, Bernard and Jô, it is doubtful he ever will. “I am going to use this anger and push myself to my limits,” said the Rio-born creative midfielder. Those limits, thankfully for Liverpool, are stretching by the week.

In fairness to Scolari and a Brazil squad that was more Fernandinho than Coutinho last summer, reservations over whether the former Vasco da Gama protégé possessed the requisite end product were still being aired at Liverpool until a few months ago. Brendan Rodgers has long championed the 22-year-old as potentially world-class, albeit with the proviso that certain aspects of his game – chiefly goalscoring – would have to improve. Sunday’s glorious winner against Manchester City showed the advice has been taken on board.

The Liverpool manager cited the security of a new contract as a factor in Coutinho’s increased productivity following the 2-1 win over the champions, a result that would have impressed under any circumstances but carried extra weight after the squad’s 4.19am return from Istanbul on Friday. The statistics support that theory. In 31 games before signing a new five-year deal in February, Liverpool’s No10 had scored twice this season. He has three goals in seven outings since.

“Phil still had three years left on his contract but we wanted to reward him for what he’s done,” Rodgers elaborated on Monday. “There will be a psychological impact from that as he feels this is the place where he’s going to spend the best part of his career.

“He wants to be here. That can have a settling effect. But before he did sign we spoke about what he needs to do to go to the next level and about scoring goals more regularly. If he can add goals consistently he’ll be right up there as a world-class talent.”

Coaching outweighs the comfort of a contract when it comes to accuracy in front of goal, however. Rodgers has been encouraging Coutinho to shoot more often all season. The problem, the manager admitted after the victory against City, is the Brazilian’s natural instinct to create rather than curl exquisite angled finishes over Joe Hart.

“He is a player that has always assisted and made the final pass in his career,” the Liverpool manager explained.

“He is a very selfless player and a very humble young guy who would rather create for others. We are encouraging him to shoot more often. He has a wonderful body movement around the box, he doesn’t need many touches to shift it and shoot, as you saw with the phenomenal shot to beat Joe Hart at that angle. His technique is at a high level so he is going to score more goals. He is now arriving into the right areas more often. He is starting to get success and that encourages him to shoot more.”

Coutinho has reflected and underpinned Liverpool’s own remarkable transformation this season. The £8.5m signing from Internazionale – £8.5m, it is worth repeating – was one of those most affected by the changes forced on Rodgers’ team during the opening four months of the campaign.

Without Luis Suárez’s movement or the injured Daniel Sturridge’s penetrating runs to look for, and Raheem Sterling not shifted into the striker’s role until November, Coutinho dwelt longer on the ball and lost possession more often.

Now his options have improved, so too his form and Liverpool’s results, and it underlines the Brazilian’s importance that Rodgers rested him for the Europa League second-leg defeat at Besiktas to enhance the prospects of a top-four finish against City.

The world-class tag remains in the distance – it was Coutinho’s intercepted pass that led to City’s equaliser on Sunday – but he has the vision to locate it plus the work-rate required.

There was a minimum of fuss over his new contract, certainly in comparison to the ongoing attempts to secure the long-term services of Sterling and Jordan Henderson, whose stunning goal against City and dominant partnership with Joe Allen demonstrated his growing influence on Sunday. And the speed of Coutinho’s contract negotiations were a reflection of his contentment at Anfield.

“I wouldn’t want to put a value on him,” said Rodgers, who believes Coutinho’s development will be measured not by goals alone but his ability to invite comparisons with the Real Madrid duo of Luka Modric and Toni Kroos.

“He offers that gold dust to how we play. If you see videos of him playing futsal when he was 11 or 12 in Brazil, he’s playing the same game now only as an adult.

“We knew he had ability, it was just about trusting that ability and allowing it to grow. He has a beautiful arrogance on the ball, his touch is magical but he’s effective and efficient with it. Playing here at Liverpool, with the dynamics of how we want to work, is perfect for him.”