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.
"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."
"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."
