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 Jamie Carragher to head back across goal, where David Ngog guided the ball with the outside of his right-foot in off the post.
It could have been two after 10 minutes, but Dirk Kuyt was unable to meet Gerrard's angled cross six yards out.
Liverpool became a bit sloppy, giving away too easily, but Debrecen could not capitalise.
The Hungarians had just Gergely Rudolf up front, while attempting to get runners in from midfield.
Debrecen had also given away a lot of free-kicks, and Dutch referee Bjorn Kuipers lost patience after 23 minutes and booked Zoltan Szelesi for a foul on Gerrard.