Kean was subjected to racist abuse by Cagliari fans on Tuesday but his 84th-minute effort on Saturday helped Juventus edge closer to their eighth successive Serie A title.
Speaking on the club’s official website, Allegri said of the 19-year-old forward: “He is doing very well, but let’s leave him to be calm.
“He needed to stay at Juventus to grow technically, train and play with the champions, but he can also improve mentally.”
Krzysztof Piatek gave Milan the lead, becoming the league’s joint-top goalscorer, before a penalty from Paulo Dybala levelled the scores after an hour.
Kean’s late intervention means Juventus are 21 points clear at the top of the table, with second-placed Napoli having just eight games left.
Allegri added: “It was important to win today, now we just need a win or a draw, in the event that Napoli does not win all the matches.
“In the first half there was little or nothing, we were a bit ‘arranged’ and I knew we could have had some difficulties.
“We were more orderly in the second half, with a good game plan, we rearranged the layout.”
Fourth-placed Milan have gone four games without a win but boss Gennaro Gattuso was satisfied with his side’s showing at the Allianz Stadium.
He told Sky Sport Italia: “It was our best performance of 2019, we lost it in the final 18-20 minutes not because Juve did well, but because of our mistakes.
“These things can happen when you play the kind of football we do.
“Even last season, we had a great performance here and the biggest regret was we were naive.”
Juventus captain Giorgio Chiellini insists team-mate Moise Kean did nothing wrong by celebrating a goal in the face of racist abuse from opposition fans during the win at Cagliari.
The 19-year-old was criticised by his manager Massimiliano Allegri and team-mate Leonardo Bonucci for the way he celebrated towards the end of a Serie A match during which he was subjected to persistent abuse, including monkey chants.
Kean stood next to the post, his arms spread wide, after netting in Juve’s 2-0 win.
There has been widespread condemnation of the criticism of Kean’s actions and Chiellini has also now leapt to the defence of the teenager.
“Moise is an asset to Italian football, a golden boy who is doing his best and he doesn’t have to pretend to be something he’s not,” said the veteran defender on the Juventus website.
“I don’t really remember what happened while I was on the pitch, but I’ve seen the pictures of Moise and he didn’t do anything wrong.
“You have to think of him like people do (Nicolo) Zaniolo, (Federico) Chiesa, (Nicolo) Barella (who are all young Italy internationals)… as a positive representation of Italian football, because he deserves that status.
“The only thing he got wrong yesterday was the dive, which I’m sure he won’t repeat, but he’s here to learn. He’s a very positive person and certainly didn’t deserve the insults he received.”
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The Italy international was abused all night by sections of the home support, with monkey chants aimed at him, but had the final say by netting Juve’s second goal with five minutes left.
The teenager stood at the post, his arms aloft in response to the chants. Juventus players, led by captain Giorgio Chiellini, protested to referee Piero Giacomelli, who was also in conversations with both managers.
Cagliari skipper Luca Ceppitelli went over to the fans behind the goal, appealing for the chants to stop, while France midfielder Blaise Matuidi appeared to gesture to manager Massimiliano Allegri he should take his players off.
When play did continue, an announcement went out over the public address system to highlight the issue, which was greeted by more jeers from some home supporters before the final whistle came after five minutes of added time.
The incident came eight days after England players were subjected to racist abuse during their Euro 2020 qualifier in Montenegro and on the day UEFA president Aleksander Ceferin insisted referees would be told to be “brave” and halt matches to stamp out such abuse from “loud, aggressive and primitive” people.
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Kean, whose goal added to Leonardo Bonucci’s towering header in the 22nd minute, was handed a start by Allegri at the Sardegna Arena with Mario Mandzukic laid low by illness
He had impressed when finding the net against both Finland and Liechtenstein for Italy, before then following it up with the winner over Empoli after coming off the bench.
Juve talisman Cristiano Ronaldo was also absent, the Portugal forward battling to be fit for the Champions League quarter-final against Ajax after a hamstring problem suffered on international duty.
Cagliari had pulled themselves eight points clear of the relegation zone following a recent upturn in form, with three successive home wins. The Sardinians, though, were soon on the back foot.
Alex Sandro, the Brazilian defender making his 150th Juve appearance, sent over a cross, which midfielder Emre Can headed over.
Martin Caceres then met Miralem Pjanic’s free-kick at the back post, but his chested effort was parried away.
Kean picked up a needless caution for simulation in the 20th minute when he went down under a challenge from Artur Ionita in the Cagliari box.
Juventus swept swept into the lead in the 22nd minute when Bonucci met Federico Bernardeschi’s looping corner with a towering header.
Matuidi then planted a header over from Mattia De Sciglio’s teasing cross out on the right as the leaders pressed again.
Cagliari finally threatened just before half-time when Nicolo Barella’s through-ball from the right found Joao Pedro in space, but his first-time shot flew just over.
Juve had a penalty shout at the start of the second half, claiming handball against Paolo Farago. However, following a quick check with VAR, play continued.
The tempo dropped as the hour mark approached before Kean surged forwards, but goalkeeper Alessio Cragno was able to stop his attempted chip.
At the other end, Leonardo Pavoletti’s header from a free-kick was glanced wide.
With five minutes left, Juve made sure of the win when Kean slotted home a low cross from substitute Rodrigo Bentancur, before taking his own stand against the racist abuse.