Chelsea assistant coach Marco Ianni confronted the former Blues coach after Ross Barkley had tucked away Chelsea's equaliser.
He allowed himself a celebratory fist-pump when Martial drove in United's second goal.
The taunting nature of the celebration did not go down well with Mourinho, who immediately bounded out of his seat as he was hauled back while trying to confront Sarri's assistant. "I want to do well for my team, players, support, I am 100 per cent Manchester United tomorrow, no more space than respect for the stadium and the fans".
"I know that Manchester United fans would never say that but Mata and Pogba in a midfield three, Lukaku, Rashford and Martial up front".
He said: "I'm not annoyed with anything".
Ianni forms part of Sarri's 10-man strong backroom staff, along with club legend Gianfranco Zola, one of two assistant first-team coaches. But then the young fellow came and he also apologised and I told him: "I accept your apology".
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Mourinho, who won three titles with Chelsea, has been touted as the next Premier League managerial sacking after his side's indifferent start to the season.
"They have to play my football, with character".
Chelsea hosted Manchester United in the first game back following the global break and the encounter didn't disappointment.
The match was overshadowed by an incident in the closing stages, with Mourinho reacting badly after being goaded by Chelsea coach Marco Ianni.
"But the defensive players also had a solid performance and again, I repeat, against a very good team full of very good players. So when he came after the game to make his apologies I accepted his apologies". Security from both sides pushed their way in and at one point Mourinho was temporarily immobilised by the bear-hug of one of Chelsea's biggest matchday stewards. I think we deserve much more than this result but this is what it is.