The 37-year-old was shown a straight red card for violent conduct after appearing to slap teammate Michael Keane just 13 minutes into the game.
Down to ten men, Everton went on to secure a memorable three points at Old Trafford thanks to a lovely goal from Kiernan Dewsbury-Hall.
Speaking after the game, Moyes didn’t seem too bothered about the altercation between his two players, admitting he ‘quite likes it.’
"I couldn’t understand it,” he said.
“I don't think anyone could have expected it. Anthony Taylor told me by the letter of the law if you raise your arm you can be sent off.
"I don't think anyone else in the stadium would have thought anything of it. I quite like it when my players fight with each other because it shows they care and (put the) demands on players. Disappointed he got sent off. He’s apologised. He praised the team and is grateful for the result. We move on.”