Liverpool's display in this opening Group E clash was way short of their best, and they were made to struggle by a team playing in the group stages for the first time.
Dirk Kuyt grabbed the winner in the final seconds of the first period, but despite dominating throughout and creating a glut of chances, Liverpool were unable to produce a convincing scoreline.
The Liverpool manager said: 'We made a lot of chances and just did not take them.
'So because of that we ended up under pressure at the end of the match when we should have been winning comfortably.
'But Debrecen can take credit for their display, this may be their first game at this level but they have dominated in Hungary for several years and you could see why.
'They were well organised and worked very hard. What we had to do was score the second goal, and then it would have been easier. But we could not manage to do that.'
But this was Liverpool's third win on the trot after a worrying start to the season.
Benitez said: 'We were in control for most of the match, they had just one shot from a counter-attack.