The 22-year-old has taken to social media to apologise for his 'ugly attitude'.
"I am aware of the ugly attitude I had," he wrote on Twitter. "I'm here to learn from my mistakes, and it won't happen again."
Liverpool eventually played out a 1-1 draw with Crystal Palace after Luis Diaz cancelled out Wilfred Zaha's first-half opener in the 61st minute.
Nunez joined Liverpool in a club record fee of £85m from Benfica after winning the Portuguese top scorer award with 26 goals.
He was on target in Liverpool's first Premier League match of the season against Fulham, which ended 2-2.
The former Almeria star is now set to miss out against Manchester United, Bournemouth and Newcastle United, he is expected to be back for the Merseyside derby against Everton on September 3.
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