The Rossoneri raced into a two-goal lead inside the opening 13 minutes but four goals from 19-year-old Domenico Berardi secured a historic victory for Sassuolo, and Riccardo Montolivo's late consolation could not stop them sliding to a seventh defeat of the league campaign.
The 18-time Serie A champion is currently 11th in the table, 30 points behind leader Juventus but more worryingly only six clear of the relegation zone, and under-fire Allegri is worried about the trajectory his team has taken this season.
"I have always worked for the good of Milan and the players, so I am relaxed with what I have done," the 46-year-old told Sky Sport Italia. "Admittedly, we are paying a heavy price this season and know the fightback will be very difficult, even more so after this defeat, but we knew the Coppa Italia was our best bet for getting into Europe.
"Obviously our position in the table is frightening, but we have to bring a different tension and concentration at particular moments in the game.
"We must start to get different results.
"The fact remains Milan should have a different position in the standings, for a series of reasons we do not, so we have to roll our sleeves up and work hard."
Milan is expected to announce Allegri's sacking on Monday, with Pippo Inzaghi reported to be the immediate successor at San Siro and former midfielder Clarence Seedorf taking over the reins in the summer.
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- Domenico Berardi