In the celebrations, Maurizio Sarri's second assistant, Marco Ianni, sprinted in front of the United bench, punching the air.
Mourinho jumped out of his seat and was held back by stewards.
That may be interpreted as implied criticism of Mourinho, but Sarri was not about to emulate his predecessor, Antonio Conte, in igniting a public feud with the former Porto, Inter Milan and Real Madrid boss.
"No, I'm not annoyed with anything", he said. "Today I was happy with the performance for 60 minutes because for 60 minutes we played our football".
"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". So, at the moment, he is better than me for sure.
When Antonio Rudiger headed the hosts into the lead all three points looked likely, but Anthony Martial scored twice in the second half to nearly give United an unlikely victory before Barkley's dramatic late intervention.
Mourinho also then gestured with three fingers towards the Chelsea fans in reference to the three Premier League titles he won for the club in two spells in charge. Then after it was 1-1 we didn't play our football, only long balls and we didn't win the second balls.More news: Kansas likely to see milder than average winter, NOAA says
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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.
"Players are different and they react in different ways to the development process and Luke reacted in the best possible way", said Mourinho.
The United manager's relationship with Chelsea supporters has strained since taking over at Old Trafford.
Fulham has now conceded 25 goals - six more than any other Premier League team - after losing 4-2 at Cardiff, which came into the game without a victory in its first season back in England's top division. While his status as a Chelsea player beyond this season may be an unknown, Blues fans will be able to delight in the form the Belgian is now in.
In the first half, United were the team so many have criticised this season.
I like Morata, he's a clever player, but I think I'd give Giroud a run of games.
"I immediately said if you really feel that way and you want to apologize, of course I accept the apology and forget it because I also make mistakes in my career".
Alvaro Morata netted the victor in the Blues' 1-0 win against Manchester United in their most recent Premier League meeting at Stamford Bridge.