As the Chelsea technical area celebrated wildly, Ianni - who later apologised to the United manager - ran towards Mourinho and punched the air in front of him before celebrating in front of the Portuguese coach.
Marco Ianni had pumped his fists in front of the United bench before there was a confrontation in the tunnel.
Substitute Ross Barkley came off the bench to score a 96th-minute leveller and preserve Chelsea's unbeaten start to the season, although the celebrations of Sarri's backroom staff visibly irked Mourinho, most notably assistant coach Marco Ianni.
With the Chelsea fans taunting their former manager - 'F-- off Mourinho!' was the chant from the main stand - he responded by displaying three fingers to his tormentors, referencing the three Premier League titles he won as the club's manager.
Marcos Alonso miscontrolled when Rudiger's through ball put him clean through on De Gea, before Alvaro Morata wasted his only big chance of another disappointing afternoon when his shot on the turn was too weak to beat his Spanish global teammate in the United goal.More news: Two tourists arrested, charged for spray painting wall in Thailand
"But if someone has to be the man, I would prefer it to be myself than my players".
"If something happened where they lost the opponent or something that made them that way because they knew it clearly which opponent was theirs".
The Portuguese made a decision to have the last word with that three-fingered gesture towards Chelsea fans - but victory would have been a much sweeter response.
"I have a certain level of education socially and in sport and what I did today, I would do in Porto, Madrid, Milan".
"If you say before the match, one point at Stamford Bridge is always a good result because it's so hard for teams to win here". Individually, in the second half, they [the players] raised the bar, especially the attacking players who brought the game into a different dimension. "I have spoken with the member of my staff and then I bring him to speak with Mourinho to say sorry to him". 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 am really disappointed in this type of performance.
"To get one point in the last minute is okay for the confidence of the players but I have to look at something else".