Allegri was sacked by Milan in January following a dismal league campaign, but the 47-year-old says that last night's victory did not represent vengeance.
He told Sky Sport Italia: "After three and a half years at Milan sharing emotions, intense moments and victories, it would've been impossible to consider this a normal game.
"Having said that, it was absolutely not a chance for revenge. Milan was an important step in my career and I am still very fond of this club.
"Now I am at Juventus and I am focused on winning with Juventus."
The Bianconeri resume their season when they host Cesena in Turin on Wednesday night.