The Intertoto Cup provided no more than a pre-season warm-up for Hibs as they were beaten by Odense on away goals.
Goals from Paul Dalglish and Rob Jones were not enough for Hibs
Trailing 1-0 from the first leg, Hibs struggled to break down their opponents and Tobias Grahn broke clear to shoot the Danes further ahead on 51 minutes.
Hibs hit back immediately, with defender Rob Jones heading in a miscued shot from Michael Stewart.
Paul Dalglish steered in a clever shot with ten minutes remaining but Hibs could not find the crucial third goal.
It is the second time in three seasons Hibs have failed to progress in the competition but manager Tony Mowbray was not too upset.
He said: "There are a lot of positives to take out of it. There was a lot of character shown not to accept defeat after they scored the first goal.
"I'm pleased the players showed our football is not about playing the same way all the time.
"They put players behind the ball in the second half so we decided to go for the long-ball option.
"With big Rob (Jones) we can be more direct. We will hopefully see the benefit of this in the coming months."
The visitors started strongly, maintaining possession impressively and denying Hibs the opportunity to get the Easter Road crowd going.
With Odense defending deep, Hibs could not utilise the pace of winger Ivan Sproule and were reduced to speculative shots from distance.
Stephen Glass tried his luck with a strike that was parried by goalkeeper Arek Onyszko and Abdessalam Benjelloun's fierce effort was expertly blocked by former Hibs defender Ulrik Laursen.
Dalglish was introduced as a substitute midway through the first-half, with striker Chris Killen being withdrawn with an injury.
Grahn gave Hibs a scare early in the second half with a shot that whistled narrowly wide and the same player then headed a great chance straight at goalkeeper Simon Brown.
However, the Swedish midfielder made no mistake with his third chance, racing on to a Morten Fevang pass to smash the ball beyond Brown.
With Hibs needing three goals to prevail, they were given an immediate boost when Stewart's wild shot flew to Jones to head past a wrong-footed Onyszko.
Kevin Thomson then went close with a measured curling shot that drifted just wide.
Glass shot over the crossbar before Dalglish set up a tense finale with a goal in the 80th minute.
The former Livingston forward managed to re-direct a shot from Steven Whittaker with a deft touch to put Hibs ahead on the day.
The towering Jones spent the final minutes playing up front but his presence was not enough to provide another breakthrough.
Hibernian: Simon Brown, Whittaker, Hogg, Jones, Murphy, Sproule, Stewart, Thomson, Glass, Benjelloun, Killen. Subs: Malkowski, Shields, Dalglish, Konde, Shiels, Stevenson, McDonald.
Odense BK: Onyszko, Ophaug, Aas, Laursen, Sorensen, Hansen, Fevang, Borre, Grahn, Borring, Timm. Subs: Lindegaard, Christensen, Oliveira, Jensen, Sturod, Larsen, Nymann.
Referee: Matteo Trefoloni (Italy)