Jürgen Klopp said Liverpool would not win the Premier League on the evidence of their dismal first-half showing against Crystal Palace after their title hopes were hit by a first home league defeat of the season.

Liverpool, comfortably beaten by Atalanta in the Europa League on Thursday, produced another lethargic display in the first period at Anfield and were punished by ­Eberechi Eze’s stylish winner for Palace, who gave their survival prospects a huge lift.

Related: Liverpool suffer huge blow to title hopes after Eberechi Eze gives Palace win

Klopp’s team, who have dropped five points in the past two top-flight games, missed a procession of ­second-half opportunities to stage yet another comeback but paid a heavy price for their profligacy and a poor opening 45 minutes. Any repeat over the final six games of the season, said Klopp, and Liverpool’s title dreams will be over.

The Liverpool manager, asked what defeat meant for the title rice, said: “The answer is pretty easy. If we play like we did in the first half, how should we win the league? If we play like we did in the second half, we can win football games. If we can win football games, we will see how many we can win and then we want to be around when the other guys struggle, if they struggle.

“We have to win games anyway. We now have a string of four away games. That would have been tough anyway and it will be tough. We have to deal with that. The criticism in these moments is completely fine, it is absolutely right. It is all about how we deal with it. The first half we didn’t deal with it but in the second half we pulled ourselves together and should have won the game.”

Klopp said there was a lack of conviction in Liverpool’s performance that originated from their two ­disappointing results away at Manchester United in the FA Cup and Premier League.

He said: “We lost in the Cup and it was like a catastrophe because we were that good and lost anyway and then we drew there and were really good. The problems we had in the United game were completely ­different to the things we had today.

“Yes, the goals we concede are too easy. That is a general thing. We all, players and me included, expected a reaction [to Atalanta] and we saw in the reaction that we lost in that game more than the game itself, so it didn’t help. We were always too wide. The goal we conceded – it ends up with Eze completely free in the box and that cannot happen. But we had other moments where we were just not together.

“In the second half we had momentum and could put them under ­pressure. The boys really tried hard but it was not enough. We have to admit that as well. The conviction and our formation was never really there for causing Palace problems.”