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.