Brendan Rodgers has said he will “fight for his life” to remain Liverpool manager and insisted his team can overcome their wretched form to finish in the top four.

Liverpool stand 12th in the Premier League having lost as many games in the opening 12 fixtures – six – as they did throughout last season’s title challenge, and have not won a league game since beating Queens Park Rangers 3-2 at Loftus Road on 19 October. Yet, despite a subsequent run that has placed Rodgers’ job prospects under scrutiny, Liverpool are only five points behind fourth-placed Manchester United.

Recent performances undermine thoughts of another Champions League qualification more than the points deficit but Rodgers believes Liverpool have the quality to transform an alarming campaign. The Liverpool manager, who will again be without the injured Mario Balotelli against Stoke City on Saturday and may rest Steven Gerrard, said: “I have an inherent belief that we can still make the top four. I know what we are all capable of here.

“No matter how we have been we are still within touching distance of the initial aim, which was fourth and then moving forward. If we are only five points off that aim then that gives me the belief that we have every chance of doing it. I’m not saying it is going to be easy. We obviously have to pick up form but what I saw from the group against Ludogorets the other night gave me encouragement that we are going to move forward.

“The players have the experience from last season and I have every belief that we can do it. Sometimes things are never as bad as people say or write. They are not always as good as people say or write either. You just have to stay calm. We will improve but we need to show it through our actions on the field.”

Rodgers admitted he was not immune to dismissal by Liverpool’s owners, Fenway Sports Group, following last Sunday’s 3-1 defeat at Crystal Palace but believes it is symptomatic of “the short-termism of modern football” that he has veered from LMA manager of the year to favourite for the sack inside seven months.

“I will fight for my life to be here for as long as I can,” he added. “You never like seeing or hearing things like you are the bookies’ favourite to get the sack when six months ago I was manager of the year but that is modern football. All I can do is my best and I will continue to do my best.

“While I do that I can relax knowing that whenever that time comes from the owners, whether it is in one month or 10 years, I will walk out of here knowing I have given my absolute all to give the club what it wants. I am happy with that.”

Former players Jamie Carragher and Bruce Grobbelaar have both been highly critical of Rodgers’ team following the dreadful performance at Selhurst Park. But the manager responded: “I’ve read a little of what has been said. You don’t forget the support you get in difficult moments on and off the pitch. I’m thankful to the unequivocal support I’ve had from legends of the club like Ian Rush, Robbie Fowler, Kenny Dalglish and Steve McManaman. They know we are in a difficult moment but are 100% behind what we are doing.”