The Brazil star was sent off after spitting at, headbutting and elbowing Federico Di Francesco in last night's 2-1 win.
Allegri fumed: "It's only right that he is fined, and he certainly will be.
"I was surprised by his reaction. We have suffered a goal, a red card and a suspension which will be long."
Costa, 28, looks set for a minimum three-match ban.
In 2015, former Newcastle striker Papiss Cisse and ex-Manchester United defender Jonny Evans were given seven and six-game suspensions for spitting.
Cisse was banned for an extra match as he was suspended earlier that season for elbowing Everton's Seamus Coleman.
Allegri condemned Costa despite suggesting the shocking attack came as a reaction to a bad foul.
He said: "Maybe he was irritated at a foul before.
"But it does not matter, because this absolutely must not happen.
"The one thing we must avoid doing is falling for provocation."
Costa apologised to Juventus fans and his team-mates but NOT Di Francesco in an Instagram post.
He wrote: "I would like to apologise to all of Juventus fans for this misleading reaction in today's game.
"I also apologise to my team-mates, who are always with me in good times and bad.
"I was ugly, I am aware and I apologise to everyone for it.
"I make it clear that this isolated attitude does not match what I have always shown in my career."
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