Nunez was shown a straight red card in Liverpool’s 1-1 draw against Crystal Palace for a headbutt on Joachim Andersen, meaning he will miss upcoming matches against Manchester United, Bournemouth and Newcastle.
It leaves Liverpool with even more problems as their squad becomes increasingly stretched just two matches into the season, neither of which they have won.
While Klopp was frustrated with Nunez’s moment of madness, and did not acknowledge the striker as he trudged off, the Liverpool boss hopes that the spell on the sidelines could prove to be beneficial for the new signing.
“Of course it was a red, he was provoked but that is not how he should behave,” Klopp said.
“Darwin knows he let his teammates down. I will talk to him. It makes no sense if I talk about it too much now in public.
“It was absolutely not a reaction we want to see. He knows he will be challenged in this way, centre-halves will do that, he’s a handful, but it is not a reaction we want.
“There’s now time for another pre-season, that’s the situation. We will use it for physical work to make him strong, not a punishment but to make him even stronger.”