Mourinho was outraged, rose from his seat and tried to confront the assistant, who appeared to disappear down the tunnel, and the United boss had to be restrained by officials.
"For the last minutes United was better than us so I am very disappointed with the last 30 minutes", Sarri, whose side remain unbeaten after Ross Barkley's last-gasp leveller, said. "To do that I would have to lose my emotional control, which is not easy", insisted Mourinho, who spent five years at Chelsea and is still respected by the majority of their supporters. "What I did here today I will do in Madrid, in Milan, in Porto, the reaction from the fans is not up to me", Mourinho told reporters.
"I am not annoyed with anything".
"I am very happy with the performance for 60 minutes because for 60 minutes we played our football", the Italian coach said. "So when he came after the game to make his apologies I accepted his apologies".
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Sarri complained that Chelsea stopped playing "his football" after Martial levelled, and were too easily panicked into playing long balls.
United's fans, however, will appreciate the efforts and intensity of their players, showing loud support for their manager as they witnessed his team finally show signs of life to build on the momentum of their comeback win against Newcastle United.
"After the match I spoke with Jose and immediately I understood we were wrong", Sarri said.
Under-fire Jose Mourinho had been on the verge of delivering the flawless response to his critics on Saturday with Manchester United closing in on a second consecutive comeback win, at the home of his old club Chelsea to boot.
City moved onto 23 points, ahead only on goal difference from similarly unbeaten Liverpool who, far from their best, were grateful for Salah's sharp first-half victor in their unconvincing slog at Huddersfield.
When asked if he rates Mourinho as a better coach than himself, Sarri told reporters: "Of course". With 7 Premier League goals, he tops the scoring charts and has been vital as Chelsea have commanded to the top of the Premier League standings next to Manchester City and Liverpool. "He was for the first time the best player of the Premier League with me, so I think the feelings are good".