John Arne Riise insists Liverpool will not give up on winning the title - a day after team-mate Jose Reina said the Reds were now playing for fourth place.
Reina and Riise have formed part of an unstable Reds defence
Keeper Reina had said the Reds were realistically looking for a Champions League spot after the loss at Arsenal.
But defender Riise said: "We never give up. Cowards give up.
"Of course, it will be hard to catch up, but at one point last season we were many points behind Chelsea, and in May we were only nine points behind."
Liverpool are ninth in the Premiership and 14 points behind leaders Manchester United but have negotiated their way into the next round of the Champions League with two games to spare.
It was neither mine nor Steven's fault that Gallas was unmarked
"Fourth place is our target now. We have to fight for that," said Reina.
"The Championship is probably too far away for us because mathematically Manchester United and Chelsea are very superior.
"We have a lot of confidence in Europe and that is a target as well. We are probably a better team in the Champions League than in the Premiership."
The 3-0 defeat at Arsenal relegated manager Rafael Benitez's side to a fifth straight away loss in the top-flight and Liverpool have only managed one point from a possible 18 on the road.
"I can not understand why we play so bad away from Anfield, I really can't," said Riise.
"Against Arsenal on Sunday, Rafa was calm in the dressing room after the match. He knew we knew that this was not good enough."
Riise also shrugged off talk of the row with captain Steven Gerrard after William Gallas added Arsenal's third when he headed home a corner unmarked.
He added: "There was some frustration in the heat of the moment, but some discussion is good. It shows we care.
"It was neither mine nor Steven's fault that Gallas was unmarked. We saw the episode on TV afterwards, and it was not our responsibility."