David Ngog's fourth-minute strike put the Reds in command of their must-win clash in Budapest.

The France Under-21 international netted from close range following a Jamie Carragher header for his fifth goal of the season.

However, Liverpool trooped off at the break aware that Fiorentina were winning 1-0 at home to Lyon, putting their future in the competition at severe risk.

And with neither game producing a goal in the second half, the fate of Rafael Benitez's side was sealed.

The Reds will therefore finish third in the group and must take a place in the Europa League round of 32 next February, with the draw scheduled for Friday December 18.

Benitez will hope his players can go all the way to the final at the Volksparkstadion in Hamburg on May 12, although his position will no doubt come under further scrutiny in the coming days after the Reds dropped out of Europe's elite.

Liverpool had Glen Johnson and Fabio Aurelio back in their side at the Ferenc Puskas Stadium, and they could not have asked for a better start to settle any nerves as they went ahead after four minutes.

Debrecen had barely touched the ball prior to Liverpool's opener, bar the concession of a couple of corners and the taking of a goal-kick.

Aurelio's cross from the right curled beyond the far post for Carragher to head back across goal, where Ngog guided the ball home with the outside of his right foot.

However, despite enjoying vastly more possession, the Reds failed to build on their advantage in the rest of the opening period, with Dirk Kuyt and Ngog both missing good chances.

It took a fine save from the Hungarian side's goalkeeper Vukasin Poleksic after 38 minutes, turning away an Ngog drive following a neat pass from Steven Gerrard, to stop Liverpool extending their lead.

After the break, Poleksic made another fine save to turn away a close range Gerrard effort after he was set-up by Johnson.

There was a scare for the visitors when Emiliano Insua lost possession to Gergely Rudolf on the edge of the box, only regaining the ball with the Debrecen forward throwing himself in the box as Liverpool's nerves frayed even further.

The hosts appealed for a penalty on 73 minutes when Javier Mascherano appeared to take down Rudolf on the edge of the box, but Dutch refeee Bjorn Kuipers waved play on.

And Rudolf threatened again nine minutes later with a powerful cross-shot which Pepe Reina was forced to punch out for a corner.

Knowing events in Florence were still not going their way, Liverpool showed little appetite for a second goal before the final whistle blew.

And substitute Adamo Coulibaly almost equalised in the dying seconds, as Liverpool's defenders allowed the ball to bounce in the area, but the Frenchman hit his shot straight at Reina.

There was an anxious wait for the Liverpool players watching the closing stages of Fiorentina's match against Lyon in the tunnel, but it eventually came to a close with the score still 1-0.

The Reds move on to Sunday's Merseyside derby at Everton, with their final Group E game at home to Fiorentina on December 9 now nothing more than a dead rubber.