The Rossoneri were beaten at home by La Viola, and Allegri said that the result was one of his lowest points as Milan boss.
"The last half-hour of tonight's game was really embarrassing," Allegri told reporters.
"It's the worst moment in my spell at Milan. 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 defeat left Milan 10th in Serie A.