كتب : Hatem Maher
Liverpool, who were already out after a miserable group stage campaign, went ahead two minutes before halftime through a near-post header from Yossi Benayoun.
Martin Jorgensen restored parity in the 63rd minute with a low shot from inside the area after some good work from Fiorentina striker Alberto Gilardino.
Italian international Gilardino gave Fiorentina all three points in stoppage time when he scored from a Juan Vargas cross.
Fiorentina have 15 points from six games, two ahead of French side Lyon who stayed second despite thrashing Hungary's Debrecen 4-0.
Five-time European champions Liverpool, who also suffer from inconsistency in the Premier League, will now play in the Europa League after finishing third on seven points.