Three minutes earlier Wilfried Zaha had thrilled a buoyant Selhurst Park crowd with his first of the season to cancel out Sadio Mane’s 49th-minute opener.
“I am not surprised at all it was tough,” Klopp said. “All our games since I am in England are always similar. We just know it is a tough place, the atmosphere is good and they don’t give up.
“We knew at half-time we had to do better. The challenge, and it’s the same for pretty much everybody, is that they come from the international teams and today I had no problem that we were not brilliant.
“In a game like this you just have to make sure you are ready to fight to get the result from the first minute.
“Could we have played better? Yes, but we had players on the pitch who on Thursday morning were still on a plane. It is not too cool and for that getting a result at Crystal Palace, who we never take for granted, is good.”
Like in the 2-1 win over Aston Villa at the beginning of the month, Liverpool again struck at the death to seal all three points on the road.
Yet Klopp is not interested in people likening the late goals to the traits of champions, adding: “I have no clue what people will say.
“I know 37 points after 13 matchdays is exceptional and you cannot have that with winning only brilliant games.
“We have had some brilliant games and we won them, thank God. But we cannot only win them so that is how it is. We are not out there to send messages – we just want to get results.”
Liverpool were pushed all the way for their victory and impressively did it without Mohamed Salah, who remained an unused substitute after a recent ankle injury.
Klopp said: “We wanted to bring him and then we scored and we were able to rest him, which is really good. Wednesday (against Napoli) he will be back.”
Roy Hodgson thought his side had taken the lead when James Tomkins headed home at the end of the first half, but VAR ruled out the effort and they went on to suffer a third straight defeat.
Hodgson was gutted for his team to walk away empty-handed, but full of praise for their display against his old club.
He said: “I thought it was our best performance of the season. We really did play well.
“It’s a bitter blow after getting what we thought was a deserved equaliser to concede that second goal from the unfortunate corner kick and take away that point we thought we were more than worth.
“It’s football. We have to learn to live with that, but I do honestly believe that was a very good team performance.”