Brendan Rodgers said Liverpool had exorcised the misery of last season’s 6-1 defeat at Stoke City after Philippe Coutinho’s magnificent late goal gave his new-look side victory.

Liverpool were heading for a point at the ground where they suffered humiliation only 77 days earlier when Coutinho, who was seconds away from being substituted having started pre-season training only three weeks ago, beat the goalkeeper Jack Butland with an unstoppable long-distance shot.

Mark Hughes claimed Stoke should have had a penalty when Nathaniel Clyne appeared to handle Ibrahim Afellay’s volley inside the area and that Dejan Lovren should have been sent off for an elbow on Mame Diouf. The Stoke manager also confirmed his club are “hopeful” of signing Xherdan Shaqiri on a permanent basis from Internazionale.

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But for Rodgers, heavily criticised by Liverpool’s travelling fans when he walked to the tunnel here in May, there was delight in a resolute defensive performance and important away victory. He said: “It is always difficult when you come to Stoke and to get a win on the back of where we were 11 weeks ago took an outstanding collective performance. Defensively we were strong and we know we have the quality to win a game.

“That [the 6-1] was a one-off, a unique game. I knew it was a one-off but it still happened and you have to be better and more resolute and we worked in pre-season on making sure our defensive organisation was better. Any coach or manager will tell you you want to get the victory but for me here it was about performing well and showing character. For me it was about ensuring the personality of the team came out. Eleven weeks ago it was embarrassing but I think that puts it to bed. Today you saw a team with determination and will.”

Coutinho’s winner was reminiscent of goals the Brazilian scored against Bolton Wanderers, Manchester City and Southampton last season. When asked whether Liverpool’s No10 can develop into a major star of the Premier League, Rodgers replied: “I think he already is. He has showed that with his quality. It was a great turn to get away from the midfield player and a wonderful shot. We were very close to taking him off, if I’m being honest.

“We felt Glen Johnson was getting space on the left side and we moved Phil up but we still wanted to win the game so we were going to make a positive change and take him off and bring Danny Ings on. I can’t profess to be any sort of genius.”

Hughes felt both sides were “happy to let the game peter out with 10, 15 minutes to go” but was aggrieved at the referee Anthony Taylor’s refusal to award Stoke a first-half penalty and to show only a yellow card to Lovren for the elbow on Diouf.

“I thought we were the better team in the first half and should have had a penalty when Afellay had a goal-bound shot and Clyne stops it with both hands,” the Stoke manager said. “That was one of many decisions we weren’t happy with.” Hughes added: “If it merited a yellow, the referee thinks something untoward has gone on and he has thrown an elbow.

“I had some sort of explanation from [the fourth official] Jon Moss and I had a quizzical look on my face because it was not an explanation I have heard before. The referee has thought it was a yellow card for an elbow. If that is the case, he was fortunate not to get a red.”

But Rodgers countered: “I have seen it again and both players were grappling for the space. Arms are coming up and unfortunately he has hit him in the face. It was certainly not intentional. He is not that sort of player.”