Alberto Gilardino scored in injury time Wednesday to give Fiorentina a 2-1 win at Liverpool and first place in its Champions League group.
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Five-time European champion Liverpool was already eliminated ahead its final group match but led in the 43rd minute through Yossi Benayoun.
Martin Jorgensen equalized for already qualified Fiorentina 20 minutes later and Gilardino secured Fiorentina's fifth straight tournament win.
Fiorentina topped Group E ahead of Lyon, while Liverpool finished third and faces the ignominy of being in the draw for the next round of the second-tier Europa League on Dec. 18 rather than the Champions League.
It is the first time since 2003-04 that Liverpool has not appeared in the knockout rounds.
"Tonight we gave a good account of ourselves and we were unlucky to lose," Liverpool captain Steven Gerrard said. "We were not good enough from our point of view.
"Now we need to qualify for the same tournament next year."
The damage to Liverpool's Champions League campaign was done by losses at Fiorentina and against visiting Lyon in its second and third matches.
Those defeats contributed to Liverpool's worst losing streak since 1987. The club's form has since steadied, but it is still just seventh in the Premier League with one win in its last five domestic matches.
It needs to finish fourth to secure a place in the qualifying rounds of next year's Champions League.
Benayoun headed Liverpool in front from a 43rd-minute free kick by Gerrard, but Jorgensen equalized with a shot past reserve goalkeeper Diego Cavalieri from a pass by Gilardino.
The Italy striker then won the match with a finish from a cross by Juan Manuel Vargas.
"At this club you try to stay in the big tournaments as long as possible, but it's gone now," Gerrard said.
