Allegri's side were 2-0 up and cruising thanks to an early red card for Fiorentina defender Nenad Tomovic.
With two points dropped in the closing stages, Allegri admitted that his side failed to control the match and missed out on an important win as a result.
He told Sky Italia: "We controlled the first half well, but when going a man up we did not deal with the situation the right way.
"The second half were not positive, as we were caught napping. It's a shame, as this could've been a very important victory to cut Fiorentina out of the race for third.
"We need to stay calm now, as we do some great things and the mistakes are part of the maturation process of this side."
Milan sit third in Serie A but will fall four points behind Napoli in second if they beat Genoa tonight.