It is the first time since 1938 that Germany has not advanced out of the group stage of World Cup play. "We were eliminated not because we didn't want to win but we never had the chance to take a lead at any point - we were always lagging behind, trying to keep up".
"The press usually just looks at the result, they criticise us a lot without knowing all the internal aspects of it, they don't know how we prepare in detail".
Like Neuer, Thomas Muller broke through the ranks in Germany's national team at World Cup 2010, although the Bayern Munich forward was benched for the crunch clash with South Korea, and the 28-year-old admitted the squad were embarrassed by their displays.
That left Germany with 40 minutes to find the one goal they needed to qualify at Mexico's expense and Kroos, their lifesaver against Sweden, just fired wide nearly at the same time the Swedes went 2-0 up through Andreas Granqvist's penalty. So, when news spread that South Korea had stolen a goal against the reigning champions, Mexico fans erupted in the stands even as their team was down 3-0 in front of them.
Kim Young-gwon's 92nd-minute goal was awarded after a video assistant referee decision.
"This is something for us to reckon with", Low said after the final whistle.
Defending champions Germany have been eliminated from the 2018 World Cup after losing to South Korea in Kazan.
And considering the country's status as defending World Cup champions, it represents a remarkable turn of fortune.
In terms of raw costs to the German economy, calculations become more complex again.
Some Mexico fans went beyond cheering while watching the action unfold television, either by waving South Korean flags or finding South Korea supporters and thanking them in person with chants and in some cases carrying them like conquering heroes.
Even though we have some good players I think it's maybe the lack of experience that we need to build on in the future.
Joachim Low made five changes from that skin-of-their-teeth win over Sweden at the weekend, but saw his side punished for yet another blunt and disjointed performance in midfield and attack.
"It was a bit of overconfidence ahead of Mexico - that we can press the button and win".