The result sees the Rossoneri rise to seventh in Serie A, while also easing pressure on the beleaguered manager.
"The team played well from start to finish," Football Italia quotes Allegri as saying. "Technically and physically we were in good shape and above all every player was at the disposal of the squad.
"After a crisis period, 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 do something good 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 has recently been linked with taking over at Napoli.