Milan are now only five points clear of the relegation zone.
Allegri said: "Fiorentina played well and kept possession, but we gifted them two goals from throw-ins. We did not react well and that is unacceptable.
"The Viola ran hard and pressed us around the field, but we were too deep and feel regret because they didn't really have many chances aside from the ones we gave them.
"It was a fairly balanced encounter. Fiorentina kept possession, but it is chances that count in football."