Liverpool are out of this season’s Champions League, despite a grinding 1-0 victory over Debrecen in Hungary.
Fiorentina’s 1-0 victory over Lyon in Italy ensured that whatever the result in Budapest, Liverpool were eliminated from the European Cup.
The Reds will now enter the Europa League (formally UEFA Cup) which they last won in 2001 under Gerard Houllier.
David Ngog got the only goal of the game just minutes into the match when he turned in a goalbound header from Jamie Carragher.
But the Reds, despite dominating possession and winning 12 corners, never really looked like adding to their early lead.
In a bizarre move, Benitez left it until the 91st minute to bring on £18million summer signing Alberto Aquilani.
Liverpool: Reina, Johnson, Carragher, Agger, Insua, Mascherano, Lucas, Aurelio (Dossena 89), Kuyt, Gerrard (Aquilani 90), Ngog (Benayoun 77).
Subs not used: Cavalieri, Spearing, Kyrgiakos, Skrtel.
Debrecen: Poleksic, Bodnar, Meszaros, Mijadinoski, Fodor (Dombi 78), Szelesi, Kiss, Szakaly (Coulibaly 62), Czvitkovics, Laczko, Rudolf.
Subs: Pantic, Ramos, Komlosi, Bernath, Varga.
Referee: Bjorn Kuipers (Holland)