But he insists that he is still the right man to turn things around after a stuttering start to the season.
Goals in each half from Juan Manuel Vargas and Borja Valero consigned Milan to their fifth defeat in 11 Serie A matches, with pressure mounting on the coach after a torrid start to the campaign.
The defeat leaves Milan 16 points adrift of third-placed Juventus in the final UEFA Champions League qualification spot and after the match Allegri was in desperate mood, with the squad now due to go into a training camp ahead of their midweek European fixture in Barcelona in an effort to reverse their malaise.
"It's the worst moment of my three and a half years at Milan," Allegri told Sky Sport Italia.
"The decision (for the training camp) was made by the club along with the coach and players.
"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.
"The last half hour of this game was really terrible. We need to get back on our feet and shake off the bad situations that happen.
"We must work and see what's going wrong, what needs changing and now the game with Chievo (next weekend) becomes very important for us, more so than Barcelona.
"When things go badly, there are many causes. The team cannot play as badly as they did here.
"We did little in attack, even if we were punished by a long-range effort that was deflected."
Allegri went on to reveal that he had heard nothing from the club in terms of a decision on his future.
"I am the coach and the club will tell me if and when they make a decision," he added.
"Right now things are going badly, we have only 12 points. There haven't been any meetings planned as far as I know. I am the coach and one way or another I’ll find the solution to this.
"In football the only thing that counts is the result. At times people forget how we got them.
"The lads cannot be criticised for the effort they put in, but it just didn't work.
"What we need to do is speed the moves up a bit, as we don't pick the right passes," the Milan coach continued.
"We take too long to get near the goal and concede far too many goals from free-kicks.
"It's normal that we have to change something and this week we'll have time to work on that.
"Right now I have to make the team feel calm. We need to be more exuberant and speed up the attacks.
"Are the players still behind me? The players shouldn't be behind me, they should be behind each other and work together as a team.
"It's my job to indicate them in the right direction."
