Juan Manuel Vargas and Borja Valero were on target for the visitors.
"Tonight we deserved the victory with a great performance and players who are settling into the squad like Vargas," Montella told Sky Sport Italia.
"We are taking advantage of all our resources and the players show great professionalism. We must not look to the past or the future, just the present. This was a delicate moment in which the team could've sought alibis, but instead the squad just sought the victory.
"We forced the San Siro crowd to be impatient, as we allowed Milan nothing and as time wore on they started to grumble.
"Milan never looked able to get back into the game, as Fiorentina seemed to be in total control, even if we were a little tired in the second half and didn't go on the counter as much."
For the big stories and the banter follow us on Twitter: @tribalfootball