Ederson, City's Brazilian goalkeeper, argued with Mourinho in Portuguese before clashes broke out between the players and staff of both clubs. The melee was dispersed by police and stewards shortly after.
Unconfirmed reports on Sunday night suggested Mikel Arteta, a member of Pep Guardiola's City backroom staff, was left with a cut to his eyebrow.
Mourinho subsequently held television interviews and a post-match press conference but made no reference to the incident, instead concentrating on the poor officiating which he felt was to blame for his side's defeat.
Goals from David Silva and Nicolas Otamendi, either side of a Marcus Rashford equaliser against the run of play, ultimately proved enough for City to claim their 14th successive Premier League win and open up an 11-point lead over their neighbours at the top of the table.
The United manager, however, felt his side should have been awarded a penalty when Ander Herrera went to ground under a challenge from Otamendi in the 78th minute. Referee Michael Oliver saw differently and showed a yellow card to Herrera for simulation.
United, second-best for the vast majority of the afternoon, almost found a late equaliser but both Romelu Lukaku and Juan Mata were denied by a fine double save from Ederson at the death.
“You can speak about anything you want, you can bring any football theory, you can bring stats, ball possession, everything - but, like last season, it is a huge penalty in a crucial moment of the game,” Mourinho said in his post-match press conference.
“But I also feel sorry for Michael Oliver because I think he had a good game, assistants the same. I think they came with the intention to make the perfect work, which they almost did.”
Mourinho went on to describe his side's defending for both Silva and Otamendi's goals as “disgraceful” before admitting that there was now a “significant distance” between second-placed United and the Premier League leaders.
“When you see Manchester City play you expect them to score great goals, not to score two 'disgraceful' goals,” the United manager said.
“They are the last goals you expect to concede against a quality team like Manchester City, two very bad goals - one corner, one free-kick with rebounds, incredibly lucky or unlucky depending on your perspective.
“Yes, they had much more of the ball, yes they had that apparent control of the ball, but the biggest save is the double save by their goalkeeper and the biggest decision of the game is the unlucky decision of Michael.”
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