The four-time winners, who had not been eliminated in a World Cup first round since 1938, were a shadow of their once dominant selves, managing only two goals in their three group games. "But we won't get carried away with that bit of success, and we'll continue to work hard".
"Yesterday we said there was only a 1% chance and so I told my players it really was a last-ditch effort for them and I told them that they had to fight until the end".
"We beat the world champions from the last World Cup and now I'm looking forward to the next World Cup".
In the other Group F match, in Ekaterinburg, Sweden clinched a 3-0 victory over Mexico, meaning a win against South Korea would have been enough for Germany to progress.
And Boateng, who missed the game as a result of his sending off against Sweden, has written an apology to Germany fans for their "disaster" and promising analysis into what went wrong would follow.
They became the fourth champions in five World Cups to fall at the first hurdle during their title defence. Shortly before the World Cup he extended his contract until 2022.
"This is something for us to reckon with", Low said after the game.
Belgium, Colombia on top as Japan squeeze through None of the teams had a red card. "We realise that all the teams have very good things, excellent players". We were fully committed and maybe because we were fully committed, we got more yellow cards.
Germany began the second period strongly, and Hyun-Woo Jo was called into action three minutes after the restart.
Mats Hummels headed over the top when unmarked six yards out in the closing stages, before South Korea's two late goals. And despite the win, South Korea does not advance either.
And Loew, the 58-year-old who guided Germany to the world crown in Brazil four years ago, admitted he now needs time to decide whether his 12-year reign will continue - despite signing a new four-year contact in May.
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.
South Korea will be one of the favourites to win the tournament, which begins in early January and runs until early February - which is a blow for Tottenham Hotspur.
Both goals were scored in injury time after a tense 90 minutes in which Germany dominated possession and South Korean fans cheered at the slightest chance of a shot on goal.
With Sweden continously leading over Mexico it meant Germany desperately needed goals.
"We need to analyse this and it has to be said very clearly that we just do not deserve it".