A 2-0 loss to South Korea on Wednesday saw them finish bottom of Group F, their first group stage exit since 1938.
“It is a really, really bitter evening for us,” Hummels said.
“The situation is very difficult to put into words,” he told ZDF.
“We did not put the ball in the net, even though we had plenty of opportunities, including myself in the 86th minute – I have to score from chances like that.
“It is a very bitter evening for us and for all German football fans.
“We believed in it until the very end, we tried to shoot, but we just couldn’t get the ball in.
“We had plenty of opportunities, we broke our necks trying out there today.”
Germany were the reigning World Cup champions heading into the tournament, and qualified on the back of a perfect record of 10 wins during European qualifying, but Hummels says they haven’t played well since sealing their spot at this summer’s tournament last year.
“We put ourselves in this situation after the Mexican game,” the Bayern Munich defender said, referring to Germany’s 1-0 loss to Mexico in their tournament opener.
“The last game we delivered a good performance was in the autumn of 2017.”
Meanwhile, midfielder Sami Khedira acknowledged that he and his teammates Germany had simply failed to live up to the expectations of being defending champions in Russia.
“This is one of the most difficult moments for the team and me personally,” the Juventus midfielder said.
“Before the tournament, we said that the world champions have to lead the way.
“That is not easy to do, but we didn’t take on the task.
“Personally, I am one of the first to take responsibility and we now have to live with the consequences.
“The last 10 years have been sensational,” he added.
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