0906 GMT June 17, 2019
Sections of home supporters left their seats after Scott Dann headed Palace ahead eight minutes from time, BBC reported.
"Eighty-two minutes — game over," said Klopp, who suffered his first defeat as Liverpool boss.
"I turned around and I felt pretty alone at this moment. We have to decide when it is over."
Dann's header saw Palace go above Liverpool in the Premier League table and means Klopp has won three, drawn three and lost one of his first seven games in charge.
Former Borussia Dortmund manager Klopp — who said that the club must calm down after it conceded another late goal against Southampton in October — was not angry with the fans who left, but frustrated with his players for not making the team believe that a comeback was possible.
"I am not disappointed about this, the fans leaving, they have reasons," said the German. "But we are responsible that nobody can leave the stadium a minute before the last whistle because everything can happen.
"Between 82 minutes and 94 you can make eight goals, if you want, but you have to work for it.
"That is what we have to show and we didn't."