At the other end, Barkley hammered home deep in injury time after a David Luiz header hit the post.
The Portuguese coach has lost on each of his three visits to former club Chelsea since talking over at Old Trafford in 2016. In any case, United's manager was not in a mood to prolong the argument.
Chelsea snatched out a draw against Manchester United in a four-goal thriller on Saturday. He first punched the air while looking directly at the United manager.
Asked if he got respect from the Chelsea fans, Mourinho said: "No, I don't think". "So we'll take it". But I have that situation immediately [after the match]. I told him to forget it. I want to play with short passes. He then ran back towards the Chelsea technical area in front of the United boss, at which point he reacted furiously.
But the under-pressure United boss, who had looked set to earn a major win on the road until Barkley's late intervention robbed United of victory, described the late setback as an "awful" result for his side. Then the young fellow came and apologised and I told him I accepted. It may fall to the club's hierarchy to make the call rather than Sarri himself.
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However, both teams are yet to play their 9th game of the league season, and they might go ahead of Chelsea if they manage to win.
Instead, it was United who took control with two goals from a renascent Anthony Martial and a second-half display that - until the late, dramatic twist - was probably summed up by Mourinho stepping on the pitch to give the forward a congratulatory slap on the back for chasing down an opponent.
"We controlled that very, very well".
In the first half, United were the team so many have criticised this season. I spoke with the member of staff and I have to be very hard. He said: "We are not organised like this". They carried more menace in the second half, but their inability to deal with the first ball, second ball or even third ball was grotesque when it mattered most.
"I think they're a near miss, I think they're one player away". "We didn't sleep in the hotel, everyone stayed at his own house, and I think the players when they woke up - because they read on social media - the pre-match was not easy for them". I am really disappointed in this type of performance.
I spent good matches prior to now, however now the one distinction is that I rating a variety of objectives, so I feel I am stronger now as a participant.