Liverpool crashed out of the Champions League after a bitterly disappointing victory in the Hungarian capital.
They needed to win to give themselves any chance of reaching the last 16, but events in Florence ended those dreams with Fiorentina achieving the victory they needed to qualify.
David Ngog scored Liverpool's early winner, but they struggled painfully to produce a convincing display, the damage having been done in two games against Lyon that cost them four points.
The road to Madrid, where the Champions League final is due to be played, now becomes the road to Hamburg - where the new Europa League will reach its conclusion - with Liverpool in with the likes of Valencia, Benfica and neighbours Everton.
The Reds' reliance on Lyon to make a game of it in Florence proved misplaced and they failed for the first time in six seasons under Benitez to reach the last 16.
It was the end result everybody expected on the night but Liverpool left the Hungarian capital deflated.
The cost is little more than a couple of million pounds this season for Liverpool, who continually stress that they never budget for anything but the group stages.
But it is a severe blow to the esteem of a true European power who have suffered a fall from grace few would have predicted when the competition started in September.
The true damage comes next season if they fail to finish in the Premier League's top four, something they are far from certain of. That would see them lose a cool £10m immediately and put further question marks over the financial direction the club is facing.
Liverpool had Glen Johnson and Fabio Aurelio back from injury, otherwise it was the same side that drew with Manchester City on Saturday - with Ryan Babel out with an ankle injury and Yossi Benayoun on the bench, suggesting that his hamstring injury is still not completely healed.
Debrecen made eight changes from the side that beat Honved in the Hungarian league at the weekend, and included seven of the side that lost 1-0 in the opening group match back in August at Anfield.
And Liverpool could not have asked for a better start to settle any nerves as they went ahead after just four minutes with the Hungarians having barely touched the ball.
Aurelio's cross from the right curled to the far post for Jamie Carragher to head back across goal, where Ngog guided the ball with the outside of his right foot in off the keeper and the far post.
Twice Dirk Kuyt narrowly failed to get on the end of close-range crosses as Liverpool sought a second.
But they began to get sloppy, giving the ball away with over-ambitious passes which wasted the impressive movement that had Debrecen struggling.
Debrecen also gave away a lot of early free-kicks as they struggled to contain Liverpool, and Dutch referee Bjorn Kuipers lost patience and booked Zoltan Szelesi for a foul on Gerrard.
Vukasin Poleksic twice saved well from Ngog, with Liverpool having 70 per cent of the possession.
But news of a Fiorentina goal against Lyon was enough to silence the travelling support and change the mood.
Debrecen's first opportunity soon followed with Gergely Rudolf heading wide when unmarked in the area. Liverpool needed, at least, to settle the issue with a second goal in this match as Debrecen continued to grow in confidence.
Poleksic made another fine save to turn away a close-range Gerrard effort after he was set up by Johnson.
Debrecen then sent on striker Adamo Coulibaly in place of Peter Szakaly. The big Frenchman had caused Liverpool plenty of problems earlier in the season.
Now nerves were getting to the Liverpool men as they toiled to clinch the match.
Emiliano Insua lost possession to Rudolf on the edge of the box, regaining the ball as the forward threw himself down in the box.
Agger's run set up a chance for Gerrard but he drove high over from the edge of the box.
Debrecen players were going down at every opportunity now, drawing howls of anger from the home fans.
Benayoun came on for Ngog after 77 minutes, with Debrecen replacing Marcell Fodor with Tibor Dombi a minute later.
Carragher headed an Aurelio corner just wide but the second goal remained elusive for Liverpool.
Kuyt was now the central striker with Benayoun on the right, but it was Liverpool on the defensive as Rudolf forced Jose Reina into a save from a fierce angled drive.
Liverpool sent on Andrea Dossena for Aurelio with a couple of minutes left, Alberto Aquilani replacing Gerrard in injury time.
There was still time for Coulibaly to have a shot kicked clear by Reina as Liverpool clung onto their lead.Reuse content