Shelbourne bowed out of the Intertoto Cup, despite a 1-0 victory at Tolka Park this afternoon in their second round second leg match against Odense.
The Danish side led 3-0 after last week's first leg, and Pat Fenlon's men were unable to overcome the deficit.
Former Cameroon international midfielder Joseph Ndo gave the eircom League side hope with a 32nd-minute goal.
But Shels, fourth in their domestic league, were unable to repeat their European heroics of last season, when they reached the second qualifying round of the Champions League before losing to former champions Steaua Bucharest.
Fenlon's men started brightly and Owen Heary went close to getting the goal they badly needed in the 21st minute.
But Irish hopes were raised when Ndo did make the breakthrough, tapping home past Odense goalkeeper Arek Onyszko.
Two minutes after the goal Stuart Byrne almost doubled the advantage - but he headed just over.
But the Danes, for whom Morton Fevang scored a hat-trick in the first leg, always looked capable of netting themselves and it needed some good Shels defending to keep them at bay.
The home side lost their way towards the middle of the second half and Fevang almost grabbed his fourth goal of the tie in the 63rd minute - but home goalkeeper Dean Delaney made an important save.
Forward Mads Timm, released by Manchester United last summer after a spell on loan at Norwegian club Viking Stavanger, came on as a substitute for Odense in the 68th minute.
Fenlon's side finished strongly and Byrne went close in the dying minutes.
But Onyszko held firm during four minutes of added time as Shels' bid to continue their European run for another season ended in frustration.