On his home Premier League debut, the 23-year-old lost his cool midway through the second-half, flooring the Palace defender and receiving a straight red card.
Liverpool were trailing at Anfield on Monday night thanks to Wilfried Zaha’s opener but went onto rescue a draw through Luis Diaz.
Nunez, Liverpool’s club record signing, broke his silence over the incident on Tuesday night, writing on Twitter: ‘I am aware of the ugly attitude I had. I’m here to learn from my mistakes and it won’t happen again.
Another tweet added: ‘Apologies to Liverpool all. I’ll be back.’
A red card for violent conduct is expected to earn Nunez a three-match suspension – starting with Liverpool’s visit to Manchester United on 22 August.
Liverpool are already without Roberto Firmino and Diogo Jota due to injury with Virgil van Dijk insisting Nunez must ensure he does not repeat Monday’s mistake.
‘He has to control himself, definitely,’ van Dijk said. ‘He has to manage himself [and] he has to be knowing that these things can happen, especially in the Premier League.
‘Obviously he was disappointed and also probably with himself. But it’s a learning curve and we will always back him. He knows it should not happen again and hopefully it will be that way.’
Liverpool boss Jurgen Klopp said of the incident: ‘I saw it now back and it’s an obvious red card.
‘He was provoked all the time, but that’s not what you should do, not how you should behave.’
Asked how much Nunez let his team down, Klopp said: ‘He knows that now himself. I will talk to him, it makes no sense for me to talk in public.
‘It is absolutely not the reaction you want to see. The challenge from the centre-back in the Premier League, they will do that to you. He is a handful himself. That’s not the reaction.’
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