Captain Steven Gerrard has told Liverpool to 'forget about the title' and focus on qualifying for the Champions League instead.
The fifth-placed Reds are three points behind city rivals Everton and level with Aston Villa and Manchester City in the battle for fourth.
Amid speculation about the future of manager Rafael Benitez, Liverpool have won only one of their last seven Premier League games.
Gerrard told the Daily Star: 'We realise now that we're facing a big challenge to finish in the top four. We've got to forget about the title and focus on fighting for fourth place.
'There are a lot of teams around us who are in good form and playing well, so it's important that we don't let our standards drop.'
Former Liverpool midfielder Jamie Redknapp does not think the Reds will ever win the title under Rafael Benitez.
He told Sky Sports: 'I don't think Liverpool can win it under Rafa Benitez. I think they are further away than they have ever been before. They have got no chance.
'For Rafa Benitez, the kudos is winning the Champions League. That's his priority, everything is geared to that. Liverpool under Rafa can beat anyone on their day. But over the course of a league season they struggle.'
He added: 'I really thought that this could be their year.
'But the rotation - they make so many changes and you don't get consistency or understanding. The best managers like Arsene Wenger and Sir Alex Ferguson keep basically the same team and system. In their big games, they field their strongest team.
'When Crouch and Torres play up front, they look as if they can make it work. They get one or two games together, but then Benitez changes it.'