Although the tie is evenly poised, it will be a tough test in the second leg next Tuesday for the Reds to progress.
They did however, manage to prevent the visitors from scoring an away goal to keep the tie very much alive.
They may not have clinched a win, but this was a superb effort from Tommy Breslin's side against a team which reached the Group Stages of the competition five years ago.
The Reds will reflect on what might have been with both Chris Curran and Joe Gormley denied by keeper Nenad Novakovic who produced two fine saves to keep the sides level at the break.
The home defence looked solid throughout the 90 minutes, rarely troubled but had to rely on the woodwork when Ibrahima Sidibe did connect from close range.
Then in the dying seconds of the game sub Sevdi should have spoiled Cliftonville's night but with a gaping goal facing him he lashed the ball over the bar.
Earlier Novakovic kept up his heroics between the posts to keep out goalbound efforts from Curran and Ronan Scannell.
Debrecen's best chance came in the depths of injury-time when, with the goal at his mercy, substitute L'imam Seydi lashed wildly over the bar.
A superb effort from the Irish League champions who can go to Hungary next week hoping to apply pressure with an away goal.
Cliftonville: Devlin, McGovern, R. Scannell, Johnston, Flynn, Curran, Donnelly, Seydak, Catney, Gormley, Cosgrove.
Subs: Brown, McMullan, Garrett, Smyth, Winchester, Murray, Caldwell.