La Viola needed a late winner to edge the Serie A strugglers today and prevail in a 3-2 thriller to earn their fourth consecutive league win.
Montella believes that his side are capable of completing an unlikely return to the Champions League if they can improve away from home in the final third of the season.
He told Rai Sport: "We have matured compared to the early games this season and are more fluid in our football.
"These are three important points and we deserved them. It's a shame we didn't have the strength to kill off the game, but we still picked our heads up twice to fight back, so I compliment the lads.
"Serie A is still wide open, so we need to rapidly improve our form away from home."
Fiorentina are now fourth in Serie A, three points off Milan in the final Champions League qualification place.