The Florence outfit had gone ahead at San Siro on Thursday, courtesy of Giuseppe Rossi's penalty on the hour mark.
But they were unable to build on their advantage and two goals in 11 minutes from Esteban Cambiasso and Jonathan gave Walter Mazzarri's charges all three points to lift them up to second in the table.
Montella was happy with how his team had performed, though, and believes that the equaliser changed the complexion of the match.
"The only thing I didn’t like was the result," he told Sky Sport Italia. "Just as we thought we had it under control, we conceded two odd goals.
"We carried on our principles of football against a tough opponent. We seemed to have the game in hand and a few ricochets went against us. We have players who need to grow, but the team showed it is a team.
"It was our mistake to feel as if we had the game under control and allowed Inter back into it. It can happen to lose the ball in midfield and often does, if you're lucky nothing happens, if you're unlucky then you concede a goal."
Goalscorer Rossi has started the season in electric form with five Serie A goals already this term, and Montella believes that his performances will put him in contention for a recall to the Italy national team.
"He (Rossi) has the dream of returning to the national team," Montella added. "(Cesare) Prandelli will decide. Selfishly I hope he stays here so he can recover, but he dreams of going back to the national team and I hope he can be made happy."
