The 29-year-old was pleased at hitting a treble, but admitted that his side were frustrated to have missed out on picking up all three points.
"It is satisfying to get a hat-trick, but a shame about the result because we really wanted the result. That's football," Aquilani told Sky Sport Italia.
"This was my first hat-trick, so I'm taking the ball home. It was important to win today and go within a point of Napoli, but in Serie A all the teams are very difficult to beat.
"I don't know if we have something more than Napoli, but we want to catch them and if possible overtake them. We have to take it day by day, in my view we are having a strong season and hopefully we'll win the next one."
Fiorentina are currently fourth in the Serie A table and sit three points behind third-placed Napoli.