Christian Benteke scored twice for Palace to leave Liverpool in third but just two points clear of fourth-placed Manchester City.
Liverpool old-boy Christian Benteke scored twice for Palace to leave Liverpool in third but just two points clear of fourth-placed Manchester City and three ahead of Manchester United in fifth.
Both Manchester clubs have two games in hand in the scrap for Champions League places, meaning Liverpool's fate is no longer in their own hands.
But Klopp believes that the Reds, who could welcome back midfielder Adam Lallana for the trip to Watford on May 1, will fight to keep hold of their top-four spot.
"The boys delivered a lot of excitement and now it's about serious football and doing what you have to do, and we will do," said Klopp, who saw Benteke's brace wipe out the lead Liverpool had taken through Philippe Coutinho's superb free-kick.
"I know a lot of people around will think 'oh my God, the Champions League slips through our fingers again'.
"Only if we let it slip. That's all I can say about this. We have tried everything and we will try everything.
"Our job is to squeeze everything we can squeeze out of this season. Obviously it's not easy for but that's no surprise.
"Maybe Adam will come back for the next game and that would help us in different situations and that is good."
Klopp, whose side lost their form just after Christmas coinciding with the departure of Senegalese star Sadio Mane to the Africa Cup of Nations, said he was used to the hard school of knocks.
"I am pretty much used to nothing more in my life than to get up after a knock," said the 49-year-old German.
"Nothing happened more often to me than this so that's no problem.
"I spoke to the boys after the game and told them it's frustrating and disappointing, we made mistakes, that's all true, and we have to feel it today, that's how defeats are.
"There is one wonderful month, a football month, to go with four games.
"We will not give up -- 100 per cent not."
Klopp had warned before the game about the dangers of Benteke, who he sold to Palace last year.
But he admitted his defenders had made life easy for the Belgian to score a goal in each half.
"Christian Benteke is an outstanding striker, there's no doubt about it, but if you leave him alone like we did for these goals I'm not sure he needs all of his skills," said Klopp.
Palace’s win was their third in succession at Anfield but it was manager Sam Allardyce's first in the league at Liverpool's home.
It left his side on 38 points and all but safe from relegation.
"We’re nearly there now," said Allardyce.
"We have 38 points after a terrific run from the players.
"We're top of the league in terms of form -- there is probably only Tottenham and Leicester as good as us in terms of what we’ve achieved over the last seven or eight games.
"We're in fantastic form at the moment.
"It was a nice one for me but Crystal Palace have won here twice before so it was another great venture for the players and our fans can travel home happy again," added the 62-year-old.