Gianluca Scamacca struck either side of half-time before Mario Pasalic capped an impressive win for the Italians in Thursday's first leg as Liverpool slumped to their joint-heaviest home defeat in European competition.
Liverpool will seek to overturn the deficit in the second leg in Italy next week and keep their hopes of a European title alive, but there is also much at stake in their meeting with Palace.
The Merseyside club are involved in a tight title race in the Premier League and sit in second place, level on 71 points with Arsenal and one ahead of Manchester City with seven games left in the season.
"The good thing about a really bad performance is that you can play better. We should start from there. I told the boys 'take it home', nobody will sleep great and tomorrow we come together," Klopp told reporters.
"The boys recover and all the others get a proper session. We go from there and on Saturday we start preparing for Palace. Yes, we have to show a reaction. Definitely, 100%, that is clear.
"But I cannot plan the reaction 20 minutes after the game. I will think about that. It is now not the first time in my life that I lost a football game, unfortunately."
Klopp made six changes to his team for the defeat by Atalanta but the recently injured trio of Trent Alexander-Arnold, Stefan Bajcetic and Diogo Jota were left on the bench.
The German said players returning from injury could no longer afford to ease their way back to full fitness, adding: "My job is not the easiest in the world, not the most difficult as well.
"It's about when you have players you need to make sure that you get them together on the pitch and then it works out somehow.
"We need them all and we need them all aggressive, fit, going for it, a bit angry, full of desire, stuff like this, and not so much dealing with your own situation, like 'I've no rhythm, I didn't play for ages', stuff like this. You have to try to avoid that."
