He told Sky Sports Italia that his side deserved better but struggled to respond following the sending-off of Gonzalo Rodriguez.
Montella said: "The team did not do badly, even if there were more mistakes than usual.
"We always took the initiative, even after going down to 10 men. Unfortunately we don't finish chances off well and all our possession doesn't lead to that many shots on goal.
"Inter were very practical, but that was no surprise. We could've done something more and this match has to serve as a lesson for the future."
Defeat at Inter means that Fiorentina drop down to eighth in Serie A after only their second defeat of the season, while Inter climb to third place.