Michael Krohn-Dehli gave them an unlikely 1-0 victory in their opening group B game against the Netherlands, and for a few brief days they were in pole position along with Germany.
But a lack of imagination and inspiration coupled with a defensive frailty already exposed in recent friendlies undermined the team and they never really recovered from a late goal that brought a 3-2 loss to Portugal in the second game.
The Danes finished third in the group after a 2-1 defeat by Germany on Sunday, a respectable result given their resources and the opposition.
"Our fans should be proud of us for a game like this. We did well this tournament, all the players did a great job, but there are still a lot of things to work on," coach Morten Olsen told a news conference.
The Danes sat back against Germany and never really pressed for the win they needed to qualify, a tactic which clearly puzzled Germany coach Joachim Low.
"Denmark plays with a real calmness, it seems as if they really don't care about the result... they stayed back a lot. They should have wanted to win the game," he said.
Much like the 2010 World Cup in South Africa, the Danes entered Euro 2012 as overachievers.
But 2010 marked the last stand for record goalscorer Jon Dahl Tomasson and influential winger Jesper Gronkjaer and, other than Nicklas Bendtner, there were few obvious replacements.
Bendtner scored two goals at Euro 2012 and set up another but often found himself lacking support as Olsen decided to shore up vulnerabilities elsewhere.
Bendtner's strength, his power in the air and his ability to hold up the ball means the Arsenal striker should have no problem finding a new club when the transfer window opens on July 1, having been on loan at Sunderland last season.
The burden of being the creative sparks in Olsen's team fell to Dennis Rommedahl and Christian Eriksen, but neither met the challenge.
Only four months old when Denmark won at Euro 1992, Eriksen found himself well-shackled throughout and, with no room to dribble or pass, he was anonymous for long periods.
His more senior counterpart Rommedahl is one of the most talented, electric players of his generation in Denmark and he is also far and away the most frustrating.
Virtually unstoppable when the mood takes him, he brought his most inconsistent form to the Euros, and was more of a burden than an asset before injury ended his tournament.
Niki Zimling and William Kvist worked tirelessly in midfield, but with no effective outlet to the wings or up front they were never able to provide much inspiration.
One bright spot for Olsen was the performance of back-up goalkeeper Stephan Andersen, who stepped up when Thomas Sorensen succumbed to a back injury before the tournament.
With only a handful of caps sprinkled over his
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