Dirk Kuyt's first-half strike was the difference between the two sides after he slotted home a rebound from a Fernando Torres strike.
Liverpool racked up 23 shots on goal with only seven of those hitting the target on a night which saw the home side dominate without playing particularly well.
Captain Steven Gerrard endured a miserable afternoon, picking up a yellow card and missing the target with numerous efforts, but Benitez insists the win is the most important aspect of the game.
"I think the main thing was to get three points," Benitez told Sky Sports.
"OK, we could have done it a little better by scoring another goal with the chances that we had, but because we didn't score (a second), we were thinking that they could've scored so it was more difficult until the end."
DominanceFor all Liverpool's dominance, their Hungarian opponents offered a genuine threat on the break as the Reds searched for an elusive second, prompting Benitez to introduce Javier Mascherano and Fabio Aurelio late on.
"Their last two or three attacks gave them some options, some hope, so I think we needed to score a second goal and always in football until you finish the game you have to be awake," he said.
The Reds boss was also keen to point out Debrecen's defensive qualities as they made a modest impression on their Champions League debut.
"I think they were well organised, efficient with intensity so it was not easy to find the spaces," added the Spaniard.
The win means Liverpool sit joint top of Group E along with Lyon, who beat Fiorentina at home by the same scoreline in the group's other game on Wednesday.