With the tie evenly balanced after a scoreless draw in Belfast, the Reds were well in the game until the home side made the breakthrough on 55 minutes following the dismissal of Jaimie McGovern.
Debrecen scored from the free kick and 23 minutes later, wrapped the game up with a second goal.
Tommy Breslin's side went into the game at the Nagyerdei Stadion very much the underdogs but determined to match the performance at Solitude that kept the tie very much alive.
Firm favourites Debrecen could not break down the Cliftonville defence and with the game still scoreless at the break, it was all to play for in the second period.
Disaster struck ten minutes after the restart with McGovern shown a red for his challenge and from the free kick Mihelic opened the scoring.
The ten men battled on bravely but could not stop Sidibe from making it 2-0 on 79 minutes.
A superb effort from the Reds, sadly just not enough for them to cause a shock on the night.
Cliftonville: Devlin, McGovern, R. Scannell, Johnston, Flynn, Curran, Garrett, M Donnelly, Seydak, Catney, Cosgrove.
Subs: Brown, McMullan, Smyth, Winchester, Murray, MGrandles, Caldwell.