Germany bowed out in the opening round for the first time since 1938 and finished bottom of Group F following a shock 2-0 loss to South Korea in Kazan on Wednesday.
Hummels sent a late header over from point-blank range, while Timo Werner and Toni Kroos also spurned chances to send the defending champions into the knockout stages before sucker punches from Kim Young-gwon and Son Heung-min.
Having surprisingly 1-0 lost to Mexico in their opening match in Russia and then required a 95th-minute strike from Toni Kroos to overcome Sweden 2-1, the Bayern Munich centre-back acknowledged they have not been at their best for a long time.
"It is very difficult to put into words. We believed in it until the end. Even after the 1-0 we still tried to turn things around," said Hummels to ZDF.
"Our problem was that we did not put the ball in the goal. Actually, there were enough opportunities - including for myself. I have to score in the 87th minute. That broke our neck in the end. We just did not use our chances.
"We have a few things to start with. I will not say publicly what they are.
"The last convincing performance we had was in the autumn of 2017. That was a long time ago.
"Today is a very, very bitter evening for us and all German football fans."
The 29-year-old criticised Germany's tactics after going down to Mexico and, although he has since seen improvements, he was frustrated by a loss of composure up front against South Korea.
"We have improved the things that I have addressed. Against Sweden it was already much better in terms of security and ball safety. We had that today, too.
"From the 65th minute we became incredibly hectic, played bad passes and were hit by many counter-attacks. There were really unbelievable counter-attacks, but we defended them well."