The defeat, coupled with Sweden's win over Mexico, ensured Germany failed to emerge from the group stage for the first time.
With Sweden concurrently leading Mexico 3-0, Germany needed just one goal to leapfrog the Central American team and continue their defence of the World Cup.
Nervous Germany increased the pressure after the break and poured forward but despite a one-sided second half they could not find the back of the net before South Korea's last-gasp double.
"We had a lot of chances, even me I should have scored in the 87th (minute)", said a rueful Hummels.
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Ettel , who did not respond to the Guardian's requests for comment on Monday, earlier defended her actions in numerous interviews. On top of all that, the mother of the young girl will apparently be pressing charges for harassment.
The loss defines what has been a disastrous World Cup for Germany, which began with a defeat by Mexico. We are sorry for not playing like world champions, and as painful as it is, we deserve to be out.
"We congratulate Sweden and Mexico on going through and South Korea on yesterday's win", the message continued.
Although very few could have expected this to have happened - it wasn't seen as a complicated set of fixtures to maneouvre them through to the knockout phase - but maybe we could have all taken a note from relatively recent history.
"I'm shocked because we didn't manage to beat South Korea and qualify", said Loew, who said he will wait for "a couple of hours" before making any decision on his future. Originally called out for offside, the goal was then given after video review.
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Why England and Belgium both want to lose tomorrow's Group G matchup
There has even been some talk that England might have an easier route at the World Cup if they lose in Kaliningrad. Belgium's attack once again shines and in this one a bit more than England's , to win the group.
From 30 yards out, it should have been fodder for World Cup-winning goalkeeper Manuel Neuer, but after fumbling Jung's dipping drive Neuer scrambled desperately to clear as Son raced to pounce.
Four minutes later, Son Heung-Min doubled the score on a counter attack, putting the ball in the wide open goal.
Mexico meanwhile thrilled in victories over Germany and South Korea but were overwhelmed by Sweden, who did well to pick themselves up after the demoralizing reverse to Low's side. The entire German nation - all of us - have lost.
With no option other than a victory to advance, Low inserted Mario Gomez and Muller for Khedira and Goretzka.
"Germany are the defending champions and No. 1 in the Federation Internationale de Football Association ranking, so I thought about what mistakes Germany might make, because they probably felt they would be able to beat us - that's what everybody thought", South Korea manager Shin Tae-yong told reporters.
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Loew, who recently signed a contract extension, said he would take time to consider his future.