The striker received his marching orders in the second half as Liverpool searched for an equalizer after Wilfried Zaha gave Palace a surprise lead after 32 minutes.
Núñez, who scored on his league debut for the Reds last week, was involved in what started as a harmless altercation with defender Joachim Andersen, but the Uruguayan striker then appeared to turn his head towards his opponent .
Referee Paul Tierney quickly waved the red card but a furious Núñez had to be sent off the pitch by his own teammates and will now face a three-game ban.
“A little provocation here and there and definitely the wrong reaction,” Liverpool boss Jurgen Klopp said after the game, adding he would speak to Núñez on Tuesday.
“A clear red card, I can’t deny that. Yeah, he’ll learn from that. Unfortunately, he’s got a few games now to do that.
“It’s not cool for us in our specific situation, let alone, but that’s the way it is.”
“I can’t really be disappointed”
Without a target man, Liverpool had an even bigger task to close the deficit, but the striker’s dismissal appeared to inflame the Anfield crowd.
Less than five minutes later, Luis Díaz waltzed past a number of defenders and fired a sensational shot from outside the box into the corner of the net to equalize Liverpool.
Despite 30 minutes of intense pressure, Crystal Palace defended well and managed to hold on to a hard-fought point.
Liverpool have now failed to win either of their first two games of the English Premier League season, having drawn 2-2 with Fulham on the opening weekend.
It means last year’s runners-up are already four points behind defending champions Manchester City, who started the season in incredible form.
“I can’t really be disappointed with the result because of the history of the game. I’m proud of the performance,” Klopp told reporters.
“It was a real [Liverpool] game, the way we started and put them under pressure. Palace had an idea, to sit deep and look for counterattacks.
“It’s really uncomfortable to play against them, especially with the quality, speed and technique they have.”
