Kean lost his head after a tussle with match-winner Gianluca Mancini, inexplicably booting the Italy defender to the ground and then heading for the tunnel to the delight of the home fans.
“In the last few minutes he could have helped us. He made a mistake, he apologised but he made a mistake because he put the team in difficulty,” Allegri said to DAZN.
“He needs to learn from this, when you come on you can make a difference. Apart from anything else it was a foul to us before and he just reacted wrongly.
“It’s not a question of frustration, Kean made a mistake, and that’s it.”
Kean’s rapid red card was not the fastest in Serie A history however, that honour being reserved for Giulio Migliaccio who lasted just 32 seconds of Atalanta’s win over Palermo in 2015.
Mancini shot Roma fourth, 12 points ahead of Juve who have little hope of Champions League football next season unless their 15-point penalty for illicit transfer activity is overturned on appeal.
Juve’s only realistic route of entering Europe’s top competition is by winning the Europa League, with the first leg of their last-16 tie with Freiburg coming up in Turin on Thursday.