TNS were dumped out of the Champions League following a 3-0 aggregate defeat by Slovan Bratislava in the second qualifying round.
The Welsh Premier League champions entered the second leg at Belle Vue on Tuesday night with a 1-0 deficit, but instead of overhauling the Slovakian club they slumped to a 2-0 loss.
Marko Milinkovic scored both goals, the first of which did not arrive until the 75th minute.
Reigning Irish League champions Cliftonville also bowed out of qualifying after Debrecen completed a 2-0 aggregate victory.
Rene Mihelic and Ibrahim Sidibe were on target as the Hungarian club plundered two goals at the Debrecen Stadium on Tuesday night.