Everton midfielder Idrissa Gueye was sent off for striking team-mate Michael Keane just 13 minutes into the Toffees' remarkable Premier League win at Manchester United.
The incident was sparked when Gueye - who misplaced a loose pass towards Keane in the penalty area to give the ball away - began berating his team-mate.
Gueye then raised his hand to Keane's face before he was sent off for violent conduct by referee Tony Harrington.
Despite his sending off, Everton went on to win 1-0 thanks to Kiernan Dewsbury-Hall's 29th-minute goal, and afterwards Gueye apologised to his team-mates in the changing room and released a statement on social media.
He wrote on Instagram: "I want to apologise first to my team-mate Michael. I take full responsibility for my reaction.
"I also apologise to my team-mates, the staff, the fans and the club. What happened does not reflect who I am or the values I stand for. Emotions can run high, but nothing justifies such behaviour. I'll make sure it never happens again."
However, Everton boss Moyes said he "likes his players fighting each other" when asked about the incident.
Moyes told SportNews: "If nothing happened, I don't think anyone in the stadium would have been surprised.
"I thought the referee could have taken a bit longer to think about it. I got told that the rules of the game that if you slap your own player, you could be in trouble.
"But there's another side to it: I like my players fighting each other if someone didn't do the right action. If you want that toughness and resilience to get a result, you want someone to act on it.
"I'm disappointed we got the sending off. But we've all been footballers, we get angry with our team-mates. He's apologised for the sending off, he's praised the players and thanked them for it and apologised for what happened."
Man Utd head coach Ruben Amorim also disagreed with the red card and criticised his players for not showing enough fight.
He said: "Fighting is not a bad thing. Fighting doesn't mean they don't like each other. Fighting is if you lose the ball, I will fight you because we will suffer a goal. That was my feeling with that red card.
"I don't agree with that sending off. We can fight with team-mates. I know it's violent conduct, the referee explained it, I don't agree with that. I hope my players, when they lose the ball, they fight each other. I hope they don't get sent off, but that is a good feeling not a bad feeling.
"My players showed in many games we can do it. Today, we didn't. I need to help them. We need to be better in the future."
Everton's match-winner, Dewsbury-Hall, called Gueye's red card a "moment of madness".
He told SportNews: "We started really well - the situation happened. It was a moment of madness, avoidable.
"But all I can say is Idrissa has apologised to us at full-time, said his piece, and that's all he can do. We move on from it.
"The reaction from us was unbelievable. Top tier. We could have crumbled, but if anything, it made us grow.
"He [Moyes, at half-time] just said: that's done now. We'll deal with that another time. It was about keeping to the plan we had. He made sure we do the right things, continue what we're doing. We can't change that now, second half we continued to do that."
However, the decision to dismiss Gueye was questioned by SportNews' Gary Neville on co-commentary.
"How much venom was in that slap?" said Neville. "He has been sent off for that. Was it a little slap or a proper whack?
"There is no doubt a hand comes out to the face but it didn't look too much. They might have had to send him off purely because there is a strike to the face.
"They were not fighting, it wasn't a scrap. It could have been dealt with by a yellow. I don't think it needed to be a red."
Jamie Carragher said at half-time in the Monday Night Football studio: "I just think: can a referee manage the situation a bit better?
"Can you get the two of them together and say: 'Hey can you behave yourselves?' Just sort of manage the situation, rather than that's the rulebook.
"The rulebook gives the referee a bit of an out. He could say: 'I don't think it's over the top' and then you can carry on 11 vs 11."
Monday Night Football guest Roberto Martinez, the Portugal head coach, agreed with the red card decision.
The ex-Everton boss said: "Clearly, it's a misunderstanding; Gueye is trying to play the ball [to Keane], but it's that reaction, the slap.
"The referee has no other choice because the law tells you that any aggression above the neck is a red card."
According to the Premier League rules, striking an opponent or any other person on the head or face with their hand or arm represents violent conduct, unless the force used was negligible.
"Was it negligible?" pondered Neville. "That's the question. I think it was negligible. I don't think there was much in that at all."
Gueye is now set to be suspended for Everton's next three games.
The Senegal international became the first Premier League player sent off for striking his own team-mate since Ricardo Fuller for Stoke City against West Ham in 2008.
It was only the third time a player has been sent off for striking a team-mate, after Lee Bowyer and Kieron Dyer's infamous double-red card in 2005.
When Bowyer and Dyer clashed in 2005, the former was handed a seven-game ban in total - an initial four games for it being his second red card of the season, before the FA handed an additional three matches to the suspension.
Bowyer was also given a ÂŁ30,000 fine, with the midfielder then leaving for West Ham in the following summer.
Meanwhile, in 2008, Stoke striker Fuller was sent off for striking his captain Andy Fuller. The striker claimed the situation actually helped team morale. Fuller stayed at Stoke until 2012.
"It's one of those things. It's done and dusted, and it's made us stronger as a unit," Fuller said.
"Sometimes in life, negatives can bring about positives, and I'm pleased that we've got by it in a positive way."
