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.
Manager Rafael Benitez said: “We had to do our job today. Our job was to win and we won but we couldn’t control the other game,” he added.
“The main thing is to be ready for the next match, we have an important game (against Everton) on Sunday.”
Liverpool managing director Christian Purslow also publicly supported the Spaniard despite the setback.
He said: “You can never predict last-minute goals, which have cost us dear in the Champions League. That’s no basis to make managerial decisions.
“We don’t run our business in that respect. I’m on the record as saying Rafa’s signed a new five-year contract, he’s four months into that contract so to discuss that is not appropriate.”
Referring to the financial aspect of missing out on qualification from the group phase, Purslow added: “It’s limited. Assuming we have a reasonable run in the Europa League then we are financially neutral for this year.”
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 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.
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 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 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.
Vukasin Poleksic twice saved well from Ngog, with Liverpool having 70% of the possession. Debrecen’s first opportunity soon followed with Gergely Rudolf heading wide when unmarked in the area as Debrecen continued to grow in confidence after the break.
Liverpool hit back as Poleksic made another fine save to turn away a close-range Gerrard effort.
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.
Then Rudolf forced Jose Reina into a save from a fierce angled drive.
There was still time for substitute Adamo Coulibaly to have a shot kicked clear by Reina as Liverpool clung onto for their win.
DEBRECEN: Poleksic, Bodnar, Meszaros, Mijadinoski, Fodor (Dombi 78), Szelesi, Kiss, Szakaly (Coulibaly 62), Czvitkovics, Laczko, Rudolf.
LIVERPOOL: Reina, Johnson, Carragher, Agger, Insua, Kuyt, Lucas, Mascherano, Aurelio (Dossena 89), Gerrard (Aquilani 90), Ngog (Benayoun 77).
Referee: Bjorn Kuipers (Holland).