David Moyes says he "quite likes" his players fighting each other after Everton's Idrissa Gueye was sent off for striking team-mate Michael Keane in the face during his side's 1-0 Premier League win at Manchester United.
United's Bruno Fernandes had just gone close to scoring when Gueye and Keane began arguing in the 13th minute at Old Trafford, with the game goalless.
Defender Keane twice pushed Gueye away before the Senegal midfielder slapped him with an open hand.
Everton's England goalkeeper Jordan Pickford separated the pair before referee Tony Harrington showed Gueye a straight red card for violent conduct.
"Do you know something, I quite like when my players have a fight," said Moyes. "I'm sort of saying I want them to be tough.
"I don't want them to accept someone not doing well enough. Someone didn't do the right thing.
"If you want a winning team, and that resilience and toughness that got us the result, you have to have players who are going to act that way."
After the game, Gueye - who is in his second spell with the Toffees - apologised on social media.
"I want to apologise first to my team-mate Michael Keane," he wrote. "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."
Moyes said Gueye's team-mates applauded when the player stood in front of the group and apologised.
"Big enough to stand up and say he made a mistake. I've accepted it, we all move on," added the Scot.
The Premier League Match Centre posted on X after Gueye was sent off: "The referee's call of red card to Gueye for violent conduct was checked and confirmed by VAR - with the action deemed to be a clear strike to the face of Keane."
The law for violent conduct defines a sending off offence as striking an opponent or any other person, on the head or face with their hand or arm, unless the force used was negligible.
However, United boss Ruben Amorim disagreed with Gueye's red card.
"We can fight with team-mates," said the Portuguese. "I know it's violent conduct because the referee explained but I don't agree."
According to Opta, it is only the third time on record (since 2000-01) a player has been sent off in the Premier League for clashing with their own team-mate, after Lee Bowyer and Kieron Dyer - for Newcastle against Aston Villa in 2005 - and Ricardo Fuller with Andy Griffin for Stoke in 2008 against West Ham.
Despite playing most of the game with 10 men, Everton won thanks to Kiernan Dewsbury-Hall's 29th-minute goal.
Match-winner Dewsbury-Hall described the confrontation between Gueye and Keane as a "moment of madness".
"It was avoidable. Idrissa has apologised to us at full-time, said his piece and that is all we can do," added the former Leicester City and Chelsea midfielder.
"We have moved on from it. It made us a grow as a team."
Everton have now won back-to-back Premier League games and are 11th in the table, above neighbours Liverpool on goal difference.
It was the first time former United boss Moyes has won at Old Trafford as a visiting manager in the Premier League, on his 18th attempt.
"I've tried coming here with 11 men and not got over the line," he added.
"It was an important win for us. We brought brilliant support here. For 80 minutes we were on the back foot.
"To get over the line took a big job."
Speaking on BBC Radio 5 Live's Monday Night Club, former Manchester City and England goalkeeper Joe Hart said "something must have been brewing" between Gueye and Keane before the red card.
"The referee wasn't even close enough to hear what Gueye was saying but he was in Keane's face, who is considerably bigger than him and shoved him off with one arm," added Hart.
"When he came over to continue the argument, the referee just casually walked over and sent him off. Jordan Pickford did very well in the situation.
"If that's all that happened though, it isn't a red card. Something must have been brewing between the two of them."
Former assistant referee Darren Cann, who officiated in more than 1,000 professional matches, described the clash between Gueye and Keane as "unusual".
Speaking to BBC Radio 5 Live, he added: "Tony Harrington was looking directly at the confrontation. He had an unobstructed view and clearly saw Gueye slap Keane around the face, so in the laws of football that would constitute to violent conduct and a red card is the right decision.
"For Keane's push to be violent conduct, it would need to be on the face as opposed to on the chest.
"Of course you can still be sent off if you punch somebody in the chest, but I would suggest that Keane's push away was more him telling Gueye to get off him."
Former Everton boss Roberto Martinez, speaking on Sky Sports, said he was "very surprised" at the clash.
"There is a bit of a misunderstanding between them," added the Portugal boss.
"The referee has no choice, the law tells you that is a red card."
Former Liverpool defender Jamie Carragher, also speaking on Sky Sports, added: "We are talking about a slap. Can the referee manage the situation [differently]? When you look at the laws, it gives the ref an out."
Former Manchester United and England defender Gary Neville, speaking on Sky Sports, said the clash was not on the same scale as "Bowyer v Dyer".
The Newcastle team-mates were sent off in disgrace for fighting during their side's 3-0 home defeat by Aston Villa in 2005.
"The major anger he showed was after he was sent off. It looked innocuous," added Neville. "My gut feeling is yellow would have been enough."
Phil in Oxford: I'm a Manchester United fan and while the little slap was quite unbelievable, I don't think it merited a straight red. A yellow card is fine. While I understand it is 'violent conduct', he is gaining no advantage by slapping his own team-mate.
Jim, Fulham: I haven't seen anything like this since Lee Bowyer/Kieron Dyer.
Alan, Aberdeen: I cannot believe Michael Keane has told Idrissa Gueye to get off and sent him on his way. There is no way that is a red card and Keane should've surely tried to defuse the situation. I'm not impressed with him.
Adam, Rotherham: It might sound reactionary, but he can't play for Everton again. That is appalling. There is no apology big enough. Some team-mates don't get on, that's life. But that performance was pathetic and immature.