The Italy international struck three times at the Artemio Franchi but his heroics were not enough to earn the Viola a win that would have drawn them to within a point of third
The Italy international twice hauled the Viola level at the Artemio Franchi, converting a penalty after Alberto Gilardino had opened the scoring from the spot and then striking again just before the break following Luca Antonini's goal.
Aquilani completed his hat-trick in the 57th minute but Sebastian De Maio secured a draw for Genoa, much to the frustration of the hosts, who had been hoping to close to within a point of third-placed Napoli.
"The hat-trick is of great satisfaction to me, but it's a shame about the result," the 29-year-old midfielder told Sky Sport Italia.
"I will sign the ball and then take it home with me, but today we were counting on a victory.
"However, football in Italy is difficult. There are teams that arrive here and defend.
"It's a pity because we would have gone to within a point of third place.
"Can we still battle it out with Napoli? I hope so. We have a great desire to overhaul them."
Fiorentina's next Serie A outing is a trip to the Sant'Elia next weekend to take on Cagliari.