Nunez was dismissed in the 57th minute for a headbutt on Palace defender Joachim Andersen, with Liverpool trailing to Wilfried Zaha's first half strike for Patrick Vieira's side.
Luis Diaz equalised for the hosts shortly after Nunez's dismissal but Liverpool could not find the winner and remain four points behind champions Manchester City after just two games.
Nunez became the first Liverpool player to be sent off on his home debut since Joe Cole against Arsenal in August 2010.
The Uruguay international will miss Liverpool's next three matches against Manchester United, Bournemouth and Newcastle United.
Klopp acknowledges Nunez was provoked but his reaction was not the best.
“It makes no sense to talk so much in public. It’s absolutely not the reaction we want to see," Klopp told Sky Sports
“The centre-halves in the Premier League will do that, they want to have him, he’s a handful himself, and that’s not the reaction.
“I don’t know how long he will be suspended, but that’s the situation and we will use it for physical work. Not as punishment, just to make him even stronger.”
Klopp added in his post-match news conference: “No, I won’t speak to him for three games!” he joked. “No, I will speak to him of course.
“I wanted to see the situation first. I didn’t know what happened. I saw Andersen on the floor and Darwin walking away. That was my view. So I asked our guys, I saw it and yes it was a red card, the wrong reaction.
“Andersen wanted that and he got it, but Darwin made a mistake.”
“A little provocation here and there, and definitely the wrong reaction. I can’t deny that.
“He will learn from that. Unfortunately he will have a few games to do so, which is not cool for us, even less with our specific situation, but it is what it is.”
