Dirk Kuyt's 12th goal in 35 Champions League games for Liverpool saw the Anfield men claim an opening Group E victory but there was nothing to suggest a Madrid final in May is on the cards.
The Dutchman is now Liverpool's third-highest scorer in this competition and they were more than thankful for his eventual winner in the final seconds of the first half.
The Hungarian champions did their best, while Liverpool were some way short of their peak.
Rafael Benitez took charge of his 300th Liverpool match as the Reds produced their 100th victory in this competition - their first was 45 years ago - but the Spaniard would have wanted a better display than this to mark a little piece of Liverpool history.
This was Debrecen's debut in the group stages but if they cannot improve on this showing they may well not win a point.
Liverpool kept faith with the side that had produced their best performance on Saturday in beating Burnley 4-0, with Fabio Aurelio on the bench for his first involvement of the season following a knee injury.
But they were sluggish and uninspired and it took them an awfully long time in the first period to get some reward for their total domination.
In fact there were barely a couple of seconds left in the half to restart the match when Kuyt forced the ball home after Vukasin Poleksic had palmed out a Fernando Torres drive.
Before that it had been one-way traffic towards the Hungarian champions' goal.
Such was the general wastefulness, even Steven Gerrard was squandering chances regularly. Three efforts sailed wide, a header dropped over the crossbar and a low drive flashed inches wide.
Albert Riera was equally at fault. Three times he was put away, and on each occasion Poleksic got a hand on the efforts.
Gerrard even found himself booked for taking a free-kick too quickly by Portuguese official Pedro Proenca, who had clearly pointed to his whistle telling the Liverpool skipper to wait.
It was unnecessary, and could come back to haunt the England star as the competition progresses and suspensions become damaging.
And so it went on. The nearest Liverpool came before Kuyt's strike was after 30 minutes when Norbert Meszaros kicked off the line from the Dutchman after another Poleksic save from Riera.
The only time Jose Reina was called into action was to touch over a 20-yard effort from Meszaros.
Liverpool improved after the break, which was not difficult, and Gerrard smashed a swerving 25-yarder against the crossbar before Yossi Benayoun went on a brilliant run past a string of defenders before forcing Poleksic into a fumbling save at the foot of the near post.
Lucas, having another fine game in midfield, saw a powerful header flash wide but Liverpool were seemingly playing with a belief that one goal was enough.
But that is a dangerous policy, and Debrecen caused some worrying moments towards the end as they almost took advantage of a succession of set-plays.
Ryan Babel came on with 10 minutes left for Riera, his first appearance since yet another outburst over his lack of matches, and he produced one clever juggling act to fire just wide.
But Adamo Coulibaly, Debrecen's French frontman, almost punished Liverpool by forcing his way through and stabbing a shot wide after 82 minutes.
That Liverpool sent on the defensive Javier Mascherano for the inventive Benayoun with three minutes left, and then Aurelio for Kuyt in injury time, said everything about Benitez's concerns and frustrations about what he was watching.
He certainly could not afford to see a couple of points thrown away by a piece of sloppy defending and there were certainly a few of those.