The coach took pride from Denmark's run in what was regarded as the toughest group in the competition.
They started their campaign with a surprise 1-0 win against the Netherlands but could not follow up on that performance, finishing third in Group B behind group winners Germany and Portugal.
"We played a great tournament. We lost on little details, but it's also our own fault," Olsen told a news conference.
"Germany deserved to win this group so to go through we would maybe have needed to draw against Portugal.
"However Danish football made a good impression."
Denmark's hopes were raised when Michael Krohn-Dehli cancelled out Lukas Podolski's opener in the first half on Sunday.
They were composed until the Germans gained the upper hand midway through the second half before Lars Bender netted the winner 10 minutes from time.
"We were compact, we kept them from creating chances," said Olsen.
"We should have had a penalty. You are not allowed to pull people's shirt in the box," the coach added, referring to when Nicklas Bendtner claimed to have his shirt pulled by Holger Badstuber.
"There is a fifth referee but he did not react. We were unlucky but we played against a fantastic team."
Looking forward, Olsen said more Danish players needed to play in the major European leagues.
"Look at the Germans, they play in the Champions League all year round. It's a different tempo and our players are not used to that," he said.
"We need to get our players out, some waved the Danish flag and can play in bigger leagues."
