Urby Emanuelson, Riccardo Montolivo, Bojan Krkic, Stephan El Shaarawy and Giampaolo Pazzini all chipped in with goals to see off the Flying Donkeys, who could only contribute to the match via Sergio Pellissier's momentary equaliser.
“The team played well from start to finish," said Allegri after the match. "Technically and physically, we were in good shape and above all every player was at my disposal. It’s an important thing to choose the right team.
“After a period of crisis, we really needed a night like this and deserved it too. We still have to improve in some aspects, but we’re on the right track to achieve something in a season that did not start well.
“So far we have been penalised by absences, though of course I too made mistakes. I also made them in the year we won the Scudetto.”
Allegri also dismissed speculation that he could be in line to replace Walter Mazzarri should the Napoli coach leave next summer.
“I will not talk about Napoli. I’ll only say that I am happy at Milan and want to respect my contract. Now let’s concentrate on getting through to the next phase of the Champions League.”