Goals from Alberto Aquilani, Borja Valero and Mounir El Hamdaoui allowed the visitors to run out easy victors, but the former Cagliari trainer feels his side were far too sloppy.
"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 45-year-old told reporters.
"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.”
Allegri then defended his decision to grant Alexandre Pato, who missed a crucial penalty during the encounter, a place in the starting XI.
"Pato did well on Tuesday, so I thought he would grow and improve by playing more. The problem is that our style of football needs us to run at full speed, and playing every three days, we cannot do that.
"Sometimes we have to play badly and try to get a result anyway. We ought to avoid the slips in concentration. It’s a shame about the results, as we could have gone up to sixth place today and did not manage it."
Milan currently sit 13th in Serie A, only five points clear of the drop zone.