After conceding a penalty on Sunday, which Alberto Gilardino converted for Genoa, Montella's team equalised thanks to Alberto Aquilai's own spot kick only to go behind again a minute later following Luca Antonini's strike.
While Aquilani made it 2-2 before half-time and then completed his hat-trick in the second half to put Fiorentina ahead in Florence, Genoa claimed a share of the points through Sebastian De Maio in the 78th minute.
Both Aquilani and Facundo Roncaglia had chances to add a fourth goal to Fiorentina's tally but they failed to convert and Montella was clearly bemused after the match.
"I think we could've won if we had made more of certain incidents," the 39-year-old coach told Sky Sport Italia.
"I saw Facundo Roncaglia's late shot and it curved in a bizarre fashion, almost as if it had been remote-controlled to swerve wide.
"It was incredible. Maybe we're cursed."
Fiorentina (41 points) remain fourth, three points behind Napoli in the chase for Serie A's third UEFA Champions League spot.
"He has an extraordinary desire to be a protagonist," Montella said.
"He doesn't have the physical sharpness he needs yet, so I'll help him settle in gradually."
