The four-time champions finished bottom of Group F after stoppage-time goals from Kim Young-gwon and Son Heung-min secured a famous victory for the Koreans in a dramatic conclusion in Kazan.
Then, Mexicans at the game - and around the world - cheered wildly when South Korea scored its first goal.
"We deserved to be eliminated", Germany coach Joachim Loew said. "It is going to be a tough challenge but we are determined to fight till the end", said Shin.
It is the fourth time in the last five World Cups that the defending champions have been eliminated in the group stage.
Hummels, who missed their last-gasp 2-1 victory over Sweden, returned to training on Monday.
Germany, meanwhile, will be desperate to show they have finally arrived at the tournament after two indifferent performances against Mexico, which they lost 1-0, and Sweden.
"We need a couple of hours to see things clearly", Loew said.
"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".
"I've always tried to take responsibility, always tried to take the team". A mad scramble from the Germans saw Neuer charge up the pitch; unlike so many successful marauding manoeuvres from the shot-stopper, this one ended with a quick clearance towards the other goal. "We looked at their strategies for the past four days". This time we did not succeed.
"We have to admit this is a defeat". The team's bad luck in Russian Federation continued Wednesday, as Mats Hummels was unable to put away a free header from 6 yards out late in the match. Sweden and Germany both had three points, and South Korea had zero.
Rudy started against Sweden after muscling his way past out-of-form World Cup victor Sami Khedira.
With Germany desperately looking for a goal to get back in the match, Neuer joined the attack.
South Korean players swept the most-searched terms on major portals and dozens of online petitions were launched on the presidential website, urging Moon Jae-in to exempt star players, including Tottenham Hotspur forward Son and goalkeeper Cho Hyun-woo, from their mandatory two-year military service.
Loew said he had not yet reflected on the future.
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