Allegri announced over Christmas that he would leave at the end of the season but Italian media were speculating on Sunday that he might not even last that long.

“I’ve no intention of resigning,” he said. “If I had, I would have done it a while back. The club can make its judgment, I accept responsibility for this defeat.”

Speculation mounted when club director Barbara Berlusconi, the daughter of club president Silvio Berlusconi, told Italian media that the performance was unacceptable.

“It was a disappointing evening, which confirms that it’s necessary to change,” she said. “It’s not tolerable for our fans to watch unacceptable performances such as this.”

Berardi, a lanky striker with a fiery temper, had not even played organised football until he was 16. His fortunes changed when he visited his brother at university, took part in a match and was pointed out to a Sassuolo youth-team coach.

Having turned professional in 2012, he helped Sassuolo out of Serie B last season as they reached the top flight for the first time, and was bought by Juventus who then loaned him back.

Milan, who have won only five league games all season, looked to be cruising after Robinho and Mario Balotelli put them two goals ahead after 13 minutes.

Berardi began Sassuolo’s fightback in the 15th minute when he rounded Christian Abbiati to score from a narrow angle. He levelled with a clever half-volley in the 28th minute and completed his hat-trick just before the break when he got between two defenders to fire past Abbiati.

Straight after the re-start, Berardi struck again with a deflected shot to become the first player to score four goals against Milan in Serie A.

Milan dominated the final half hour and Japan midfielder Keisuke Honda hit the crossbar after coming on in the second half for his debut.

They hit the woodwork three times, repeatedly appealed for penalties and pulled one goal back through Riccardo Montolivo, but they could not force an equaliser despite five minutes of stoppage time.