It finished 2-2, with Ross Barkley scoring a late equaliser after Man United turned a 1-0 deficit into a 2-1 lead.
But in his post-match press conference, Mourinho revealed Ianni had approached him in the tunnel after the match and apologised.
"I don't think (I got the respect back)", said Mourinho on Sky Sports.
Whether he enjoys it or not, Mourinho is the guy who is always portrayed as the villain of the piece, but there was so much more to this game than the incident with Ianni and his reaction to the fans who once idolised him.
"I am not annoyed with anything". The assistant has already come to me and apologised. "But I also made mistakes in football matches and will make more".
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A scuffle then ensued as Mourinho attempted to argue with Ianni, which took a few minutes to settle down and involved over 20 players and staff. Mourinho says a lack of education was to blame, but, accepted the mistake.
Nonetheless, Mourinho has been no stranger to criticising his own team and again appeared to damn his players with faint praise when asked why they have been unable to replicate the second-half performance against Newcastle over 90 minutes.
Manchester United have lost all three of their games at Stamford Bridge since former Blues manager Mourinho took over the reins of the Old Trafford outfit in May 2016.
Former Arsenal midfielder Merson believes Chelsea FC will inflict a fourth league defeat of the season upon Mourinho and his Manchester United side to leave their rivals toiling in mid-table.
"One point at Stamford Bridge is always a good result because it's so hard for teams to win here but after the game, the way the game was, it's an bad result for us and a phenomenal result for them". I do not know where the extra time came from.
In a match which epitomised the rich history of the Premier League's drama, Manchester United came away with just one point.
Mourinho eventually returned to his seat and a second fracas kicked off between the players on the pitch at Stamford Bridge. The 2-2 [equaliser] in last minutes is okay for confidence of my players, but I have to look at something else.