The Rossoneri boss responds to comments that the cross-city rivals are too far apart in Serie A to be compared, retorting that only his side are representing Milan in Europe
The two sides have experienced contrasting fortunes in Serie A this season with the Nerazzurri sitting in sixth, nine points and five places ahead of the beleaguered Rossoneri.
However, speaking ahead of his side's trip to Sassuolo on Sunday, Allegri drew attention to the fact that only Milan remained both in the Coppa Italia and Champions League, rejecting Mazzarri's recent remarks that there is a "huge difference" between the two teams.
"A city like Milan should have two clubs playing in Europe," the 46-year-old told a press conference.
"However, we’re the only Milan club left in, as is the case in the Coppa Italia.
"At the moment Inter are ahead of us [in Serie A]. We'll just have to try to represent the city in Europe, seeing as Inter have been knocked out.
"Inter are doing well, they’ve a nine-point advantage over us and have everything in place to have a good second half to the season. But to bicker over the gap makes no sense."
Mazzarri had earlier this week revealed his irritation that Inter's season was being compared to Milan's, claiming that the Nerazzurri were far better off as things stand.
Allegri, however, feels that his under-fire players have a chance to turn their season around after their 3-0 win over Atalanta on Monday and is targeting victory over Sassuolo.
"We need another win and good performance," he continued.
"The game is very important as we still haven't won two games in a row this season."
"We mustn't forget the way we played in the first half of the season, nothing is certain in football. We have to approach the game with the right attitude or we could find ourselves in trouble.”
Milan currently sit 11th in Serie A with 22 points from their 18 games.