Unfashionable Cesena, back in Serie A for the first time since 1991, netted through forwards Erjon Bogdani and Emanuele Giaccherini before Zlatan Ibrahimovic made an awful night worse for Milan by missing a late penalty on his debut.
The team from the small city near Rimini in eastern Italy have been tipped by most pundits to go straight back down but they deserved to beat a Milan side which strengthened in the transfer window to become Serie A favourites in some eyes.
"It's a defeat which will do us good," former Cagliari boss Allegri, who replaced Leonardo in the close season, told Sky television after their second outing of the league campaign.
"We need to have a completely different attitude. You need sacrifice. When we don't have the ball we need everyone to track back and tonight I didn't see that."
Milan, who beat Lecce 4-0 in their opener, have a chance to make immediate amends in their first Champions League match at home to Auxerre on Wednesday and Cesena's coach believes the seven-times European champions will still have a good season.
"It's a win which gives us confidence but we mustn't think too much about it. I'm sure Milan will be in the title race," said Massimo Ficcadenti, whose side drew 0-0 at Roma first up.
