Nunez made his first start for the Reds after two goals and two assists in his previous two cameos, coming in as Roberto Firmino dropped out due to injury.
The 23-year-old endured a tough night in front of goal as he squandered a number of chances, before a moment of stupidity after the break in a clash with Palace centre-back Joachim Andersen.
In the tussle with the Dane, Nunez attempted one headbutt before connecting with another, rightly receiving a straight red card with Liverpool already a goal down.
Luis Diaz salvaged a point with a stunning effort not long after, but speaking in his post-match interview with Sky Sports, Klopp admitted it was “not how [Nunez] should behave.”
“That’s, of course, a red card. He was provoked all the time, but that’s not how he should behave,” he said.
“But then four minutes later, the equaliser, and a massive game for us with 10 men, putting in so much effort, the stadium was there.
“The real feeling I have in this moment is I’m proud [of the team].”
Asked whether he would address letting the team down with Nunez, Klopp added: “Look, he knows that now himself.
“I will talk to him. It makes no sense to now talk too much in public. It’s not the reaction you want to see.”
Interestingly, though, the manager looked on the bright side of a three-game ban for his £85 million signing.
“There’s now time for another pre-season,” Klopp said. “We will use it for physical work, not as a punishment, but to make him even stronger. That’s what we will try.”
In his own interview, Palace manager Patrick Vieira revealed that he was yet to speak to Andersen about the incident.
“No, we didn’t talk about it,” he insisted. “I didn’t have a chance to see it yet.”