Diego Milito’s penalty was followed by Antonio Cassano’s strike, before Romulo pulled a goal back for the visitors.
However, Montella’s side were reduced to 10 men when Gonzalo Rodriguez was given a second yellow card and as a result they were unable to muster a late fightback.
“The team did not do badly, even if there were more mistakes than usual,” the coach told Sky Sports Italia.
“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.
“It is important that we always take the game to our opponents, but we must also learn to be more effective in front of goal.
“On the other hand, 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."
Montella also felt the loss of midfielder Alberto Aquilani affected his side and pointed to a lack of creativity for their problems.
“There’s a long way to go and a lot of work to be done, but there are some promising signs. We are missing Alberto Aquilani in midfield, as he can give us something more there," he added.
“We do need a player who can score. We’ve got players who could do that and are working on them to improve these skills.”