The Uruguayan was shown a straight red card on his Anfield debut after headbutting defender Joachim Andersen part way through the second half.
The striker then reacted angrily to the decision, and had to be calmed down by teammate James Milner before leaving the field of play.
At that stage in the contest, the Reds were a goal behind following a first-half strike from Wilfried Zaha, and despite scoring an equaliser just minutes after the dismissal courtesy of Luis Diaz, were unable to find a winner.
The result now means that Liverpool have dropped four points from their opening two matches.
Reflecting on the sending off for Sky Sports’ Monday Night Football after the final whistle, both Neville and Carragher were in little doubt as to the correctness of the decision, or of the negetive impact it could have for Jurgen Klopp’s side over the course of the next few weeks, with a clash against bitter rivals Manchester United coming up in just seven days’ time.
Addressing the incident, Neville said: “It’s a moment of madness, isn’t it?
“We saw in the first couple of games, the Community Shield and the game against Fulham, he’s combative.
“That, it’s a proper ‘are you feeling that?’. That’s a proper butt, not one of those where they both put their heads together and the referee can book them both. That’s a proper butt to the underside of the nose.
“I have to say, he’ll learn a lot from that. He’s not helped his team tonight, as much as Liverpool played really well after he got sent off.
“Next week is a problem, and they’ll miss him now.”
Ex-Reds defender Carragher reiterated Neville’s point, adding: “There are moments of madness, of course there are, but when the referee is looking straight at him...
“I cannot believe how he possibly thinks he’s going to get away with that. But he’s remonstrating to the referee, the referee is looking at the incident, and he’s just looking straight at it.
“There was no other option for the referee, obviously, but he could not have had a better view. It’s literally half a second later than when he [Nunez] complained to the referee.
“Andersen hasn’t hit the floor - look at the referee, the whistle’s in his mouth to blow now, Andersen has only just been touched. That shows you what a great view the referee had.”
Carragher also went on to address Nunez’s disgruntled reaction to being sent off.
The former Anfield star explained: “What that was at the end, you’re trying to argue you haven’t done nothing - you’re trying to convince your own teammates, maybe the crowd.
“But as he’s walking back to that bench, the realisation, and he’ll be sitting in the dressing room absolutely devastated - and rightly so.
“He’s let himself down, but he’s also let his team down there. It’s more points dropped as well.
“If he’d have been on the pitch, I’m sure Liverpool possibly would have gone on to win the game.”