"A passive and anaemic Manchester United first half, second half it very almost became masterclass but it ended with Mourinho showing absolutely no class, none whatsoever", he said.
There was less than 40 seconds remaining of the six minutes of added time when Barkley scored.
Twitter reacted to the game, and here are some of the best tweets.
He said: "I'm not annoyed with anything". Then the young fellow came and apologised and I told him I accepted.
Antonio Rüdiger grabbed the lead for Maurizio Sarri's charges in the 21st minute with a powerful free header from the centre of the box after eluding his marker Paul Pogba following a corner.
Chelsea boss Maurizio Sarri reveals mixed news regarding injury issues in his first-team squad ahead of the Premier League clash with Manchester United.
"Not celebrations, bad education", the Portuguese said.
"I did not get respect back from Chelsea [fans] but that is not my responsibility".
"I don't know where they came from".
Sarri was quick to apologise to Mourinho and said he would take action behind closed doors. I have seen the match from the bench and now I have to analyse it.
I think it's fair to say that the football world had quite the mixed reaction to the game... I told him to forget it.
The club is well aware of what Mourinho achieved at Stamford Bridge and those behind the scenes are said to be very embarrassed by the behaviour of Ianni towards the man who delivered Chelsea's first domestic title in 50 years.
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 United boss, who has a tough run of fixtures coming up, including games against Juventus and Manchester City, described the draw as an "awful" result for his team, who roared back from 2-0 down to beat Newcastle United in their last match.
"It is always a good feeling when you win something".