Chelsea is top of the league because he is the kind of player who can make a huge difference.
Sarri also offered public apologies to Mourinho for the behaviour of Ianni, as he confirmed his assistant has been warned to contain his emotions.
The 22-year-old netted a brace for Man United at Stamford Bridge on Saturday lunchtime as the Reds came painfully close to achieving a first win at Chelsea in all competitions since October 2012.
Ianni did his cavorting right in front of Jose Mourinho and on his way back past the United manager was looking at him and fist-pumping pointedly and Mourinho leapt up in fury and pursued the Italian, who disappeared down the... Security from both sides pushed their way in and at one point Mourinho was temporarily immobilised by the bear-hug of one of Chelsea's biggest matchday stewards.
Pogba was at fault for Chelsea's opener after losing Antonio Rudiger at a corner to allow the defender a free header.
Manchester United manager Jose Mourinho was involved in ugly scenes at the end of his return to Stamford Bridge.
"Martial is improving, he is doing different things than before", said Mourinho.
"I think it's private. So I have to study this match very well because we can learn a lot".
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"We were on the wrong side of this and this is why we apologise", stated Sarri. If I knew I would have been able to immediately change the situation.
Sarri also said he would speak to Ianni again on Sunday.
Jose Mourinho wanted to bring in defensive reinforcements in the summer, but the United hierarchy failed to back him in the market. "Yes, [they were] not celebrations, [more a] bad education".
"The assistant has already come to me and apologized, I told him to forget it".
A decision will be made this week as to whether Ianni will be part of the staff on the bench for the foreseeable future.
"We controlled that very, very well". [We were] the best team on the pitch. But we were there, we were in the game.
"Then after 1-1, we didn't play our football, only the long ball, we are not organised for the second ball. I want to play with the short passes".
But moments after their goalkeeper Kepa Arrizabalaga had pulled off his first save of the match from former Chelsea midfielder Juan Mata in the 55th minute, United's Anthony Martial smashed in an equaliser and, according to Sarri, Chelsea's tactics went to pieces.