On-loan Chelsea attacker Mohamed Salah came off the bench to score the only goal of the game for Vincenzo Montella's men 10 minutes into the second half.
It was Fiorentina's first away win at Inter in Serie A since May 2000 and ended Inter's recent run of three consecutive league wins.
Mancini was frustrated by his team's passive first-half performance, but still felt they could have taken something from the game.
"We were generous, we know they are a good team and it was in my opinion a very balanced game," he told the club's official website.
"Had we found the equaliser immediately, maybe we could try to bring home a victory.
"The problem was that at first we were hesitant. Fiorentina are a team that dribbles well. In the first half we had to be bolder, more determined."
Inter looked a different team following the introduction of Xherdan Shaqiri midway through the second half, and the Swiss midfielder laid on a couple of great chances for Mauro Icardi and Fredy Guarin to level.
Lukas Podolski and Mateo Kovacic were less impressive in Mancini's eyes, however.
"Shaqiri did well but had played [on] Thursday, so it was right to give him rest," Mancini added.
"Podolski must give more, so it is not enough, he is the first to know that. Even from Mateo I expect more."
Inter will certainly require more from their star men when they travel to third-placed Napoli in their next league match.
