Mexico had looked good for a last 16 spot going in to the final round of games with two wins from two, but found themselves 3-0 down against the Swedes, meaning Germany could have sneaked through at their expense if they had beaten South Korea.
Germany, 2014 champions, are out of Russian Federation 2018 after group stages, their first exit in the World Cup group stages in 80 years.
"I can not say why this was for us", he told reporters. "For us, this is a huge disappointment".
Mexican fans in Russian Federation for the World Cup also expressed their gratitude to one South Korean they found outside the stadium in Ekaterinburg following the defeat to Sweden.
The Koreans needed to record a victory over the Germans and see Mexico defeat Sweden to realise their slim hopes of advancing to the knockout phase.More news: Lakers pressured to add Leonard before LeBron decision
Son played a corner into the area, with Hyun-Soo Jang flicking the ball on - past Kroos - before Young-Sun Yun's touch put it into the path of Kim at the back post, who tapped home.
Kim was not so profligate when he fired home from close range - although he was initially given offside before a VAR review sparked renewed celebrations - and Son completed the job.
The tears flowed on both sides of the field after South Korea beat Germany at the World Cup.
"Germany are the defending champions and number one 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".
Germany are the first of the favourites to be knocked out, after Spain, Portugal and Argentina all scraped through the group stage.More news: Medical milestone: US OKs marijuana-based drug for seizures
"As we saw in the match against Mexico, their players were really determined and with that mindset we can play a game we won't regret and the results will follow".
"Since we won, everything went as planned", South Korea coach Shin Tae-yong said.
Low and his players will return to Germany on Thursday, but with the coach dismissing suggestions that dark times could lie ahead.
"We did not deserve to be winning the title once again", Loew said. Shortly before the World Cup he extended his contract until 2022.More news: Apple's working on noise-canceling AirPods, over-ear headphones
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