Liverpool's worst fears were confirmed as they were dumped out of the Champions League despite winning their penultimate game 1-0 against Debrecen.
The Reds needed already qualified Lyon to win against Fiorentina in Italy to keep alive their slim hopes of progressing from a congested group.
However, after Juan Manuel Vargas's 28th minute penalty proved decisive in Florence, it left a deflated Liverpool facing up to their first failure to reach the knockout stages of the Champions League in seven years.
David N'Gog's fourth-minute goal in Hungary mattered little as Reds boss Rafael Benitez must now plan an assault on the Europa League during the second half of the season rather than Europe's premier club competition.
Elsewhere, there were no such problems for Arsenal, who confirmed their passage as Group H winners with a game to spare.
First-half goals from Samir Nasri and Denilson secured a straightforward 2-0 victory over Standard Liege at the Emirates Stadium.
AZ Alkmaar and Olympiacos played out a goalless draw in the group's other game which has left the Greek champions needing just one point from their final game to following Arsenal through as runners-up.
Meanwhile, Barcelona were the big winners on the night after moving up from third place to top spot in Group F following a priceless 2-0 win over Internazionale.
Early goals from Gerard Pique and Pedro at the Camp Nou secured only a second win of the group stages for the defending champions and left Inter's hopes of reaching the last 16 hanging in the balance.
Barca also had the luxury of leaving star players Lionel Messi and Zlatan Ibrahimovic on the bench amid concerns over their fitness following the lightening start they made to a pivotal match.
The Italian champions remain second in the group only by virtue of Rubin Kazan and Dynamo Kyiv playing out a goalless draw in Russia earlier in the day.
However, Jose Mourinho's side will still progress to the knockout stages should they avoid defeat at home to the newly-crowned Russian champions at the San Siro in their final game.
Meanwhile, Rangers will not be able to look forward to European football after Christmas following a costly 2-0 home defeat at the hands of Stuttgart.
Walter Smith's side needed to win to stand any hope of securing third place in Group G and a place in the Europa League.
However, Stuttgart and Unirea Urziceni will now fight it out for second and third in that group on the final matchday after the Romanian side edged out already qualified Sevilla by a 1-0 scoreline.