But Barkley's 96th-minute equaliser caused wild celebrations, with Ianni jumping around in front of the United bench, eliciting an angry response from Mourinho.
He later held up three fingers to the Chelsea crowd, signifying the three Premier League titles he won with the Blues.
Mourinho said after the game that Chelsea manager Maurizio Sarri told him on the field that he would handle the issue internally, and that Ianni later apologized to him for his behavior.
"And after that Sarri's assistant came to me and apologised to me".
"I spoke with Jose afterwards and realised we were wrong", Sarri said. So of course, I have to speak [to him].
Following the game he said: "My confidence has grown but our target was to win the game so it is disappointing. I understood that we were in the wrong side of the situation", Sarri told BBC sport.
United had taken a 2-1 lead thanks to two goals from Anthony Martial after trailing at the break.
In a match which epitomised the rich history of the Premier League's drama, Manchester United came away with just one point.
"But I have made many mistakes in football matches, especially when I was younger, and I will make many more so when he came to apologise I accepted".
Asked if he had received the same level of respect he had shown to Chelsea, Mourinho said: "No, I don't think [I did], but that's not my responsibility". But the Chelsea manager did not know the precise nature of Ianni's actions until he spoke to Mourinho after the game. "It looked like we could have scored in six or seven situations but we needed one better pass".
The altercation overshadowed the dramatic Chelsea comeback but also a much-improved Manchester United performance.
While Jose Mourinho's side are undoubtedly in poorer form now, should they be rated less likely to beat this Chelsea team than last season's record breakers?
Mourinho demonstrated he can still provoke a reaction from these United players as they responded to his half-time talk with a transformed second-half display, full of pace, threat and intent, which took them to within seconds of an outstanding win.