The beleaguered Rossoneri coach admitted his side's second-half showing against the Viola had been 'embarrassing' but he refused to pin the blame on a low-key transfer window
Juan Vargas and Borja Valero struck either side of the break to heap more misery on the Rossoneri, who have now lost five of their 11 Serie A games so far this season.
But though fans unfurled offensive banners and hurled insults at the team after this latest setback, Allegri does not regard his position as untenable, and is optimistic a planned training camp will get Milan back on track.
"The last half-hour of tonight’s game was really embarrassing," the 46-year-old told reporters after the game. "It’s the worst moment in my spell at Milan.
"When things go badly, there are many causes. The training retreat is not a punishment. It will help the team to take more responsibility. We need to get back on our feet.
"I can only thank the fans as they always support us. It's only normal that they protest after a defeat like this one.
"The team cannot play as badly as they did tonight. We need to find the solution to get out of this moment. Staying together will help us prepare for Barcelona and Chievo, above all psychologically."
Critics have been quick to blame lacklustre transfer activity as the cause of the San Siro giant's downfall, but Allegri has stood by the club's summer dealings, preferring instead to pin the blame on injuries.
"It hasn't got anything to do with the transfer market. We have had many injuries and we have to regain our balance," he reasoned.
"We’re missing [Stephan] El Shaarawy, so we don’t have many options out wide at the moment. The players can't be criticised for the effort they put in tonight.
"It was just one of those nights where it just doesn't work. Right now I have to make the team feel calm. We need to be more exuberant."
Allegri won the Scudetto in his first year in charge, but barely secured Champions League qualification last term after the departures of Zlatan Ibrahimovic and Thiago Silva to Paris Saint-Germain.