Despite an ultimately comfortable scoreline that drew Liverpool level on points with league leaders Manchester City and second-placed Arsenal, the visitors' shaky backline was badly exposed at Selhurst Park at times.
Dejan Lovren was at fault when James McArthur cancelled out Emre Can?s opening goal and the centre-back later allowed the Palace midfielder to head his second goal after Lovren himself had restored Liverpool's lead.
Saturday's result meant the Reds have kept just one clean sheet in the league so far this term, but Liverpool manager Klopp said: "We will sort the defence. When that happens, we will see (if we can challenge in the league).
"They can defend really well -- it's normal (to have lapses). But I know that everybody will talk about this."
The German said that singling out individual players for criticism was not his style, adding the way Liverpool responded to their early errors against the Eagles demonstrated the team's resilience.
"I don't go in the dressing room and say, 'You're a really bad defender, and you are the goalkeeper, where are you?'," he explained.
"They are all human beings, we work on it. I am completely convinced about the quality. If they make mistakes and stay in the game, then it's a very good test for them, and they stood it again.
"I was happy with the reaction. Not with the situation, not with the style of the game, that's what we have to work on, but I'm happy with the reaction."
Klopp hails Coutinho
Lovren's fellow central defender Joel Matip put Liverpool ahead for a third time immediately before half-time and Roberto Firmino wrapped up the win midway through the second half.
But Philippe Coutinho was the game's outstanding player and Klopp praised the contribution of the Brazilian international.
"He?s a very good football player. His work-rate is outstanding. That's important for the team, and you cannot change this because you cannot be a genius every day,? he said.
Meanwhile home manager Alan Pardew was left frustrated by his side's failure to capitalise on Liverpool's mistakes, with Palace paying a heavy price for their own errors at the back.
After a successful September when they recorded three wins, the south London side have lost three games on the run and need to end that sequence if they are to avoid getting dragged towards the lower reaches of the table.
"McArthur was exceptional, he scored two goals and his energy levels were a positive force for us all game," said Pardew.
"But at times the back four looked like it will need some work today," the former Palace midfielder added.
Pardew also questioned Andre Marriner's appointment for the match, after the referee awarded Liverpool a contentious penalty converted by Christian Benteke -- now at Palace -- in last season's corresponding fixture, which the Reds won 2-1.
Saturday saw Marriner turn down three Palace penalty appeals and Pardew said: "I don't think Andre Marriner should have reffed this game. He gives the penalty last year so we've got a negative in our mind anyway.
"And then we get three penalty calls, okay they are tight, but they are probably no worse than Christian's last year, so it's just a little bit frustrating that part."
As for Liverpool's chances of winning a first English title since they lifted the old First Division trophy in 1990, Pardew added: "They are certainly going to be close.
"Their two centre-halves are terrific, even if they made a mistake. That's an area they are not so strong, but they played well.?