Germany lost a World Cup penalty shoot-out for the first time as they crashed out of the last 32 to underdogs Paraguay.
Kai Havertz cancelled out Julio Enciso's first-half opener, but the Arsenal forward, along with Newcastle's Nick Woltemade, had their spot-kicks saved by Orlando Gill before Bayern Munich defender Jonathan Tah blazed over, allowing Jose Canale to set up a last-16 tie against France or Sweden.
Germany have not won a World Cup knockout tie since winning the competition for a fourth time in 2014 and were harshly denied by a controversial VAR decision in the second half of extra-time when Tah's powerful header at a corner was ruled out for a soft foul by Waldemar Anton on Gill.
But Julian Nagelsmann's side delivered a dismal first-half showing in which they failed to have a shot on target and went into the break behind despite having 78 per cent possession.
They could only improve yet, having won all four of their World Cup shoot-outs, still couldn't rely on penalties, even when Paraguay squandered two opportunities to win it as Antonio Sanabria sent his effort wide and Manuel Neuer saved from Fabian Balbuena in an epic finale.
Germany boss Julian Nagelsmann said:
"I am not someone who runs away. This is not the first time this has happened, and there are some things about today that need to be changed.
"But if the DFB wants me to continue, I am going to continue. I know the mechanics of football, I know how the industry works. I know a lot of people will want me to leave but I would love to continue if the football association wants me to."
Germany striker Kai Havertz said:
"I'm a little lost for words. This is my second World Cup and both times it came to nothing. All I can do is apologise.
"We have to take a hard look at ourselves, especially the players, and I'm leaving the coach out of that."
Paraguay defender Gustavo Gomez said:
"The feeling is hard to explain. I'm very proud of my team-mates, of the group.
"I'm most impressed by our unity. We have incredible strength to face any situation. Germany knew they needed to work incredibly hard to beat us."
Sky Germany reporter Florian Plettenberg speaking on Your Site News:
"I have to admit I'm completely shocked. It's a complete disaster again. After the World Cup in Russia, after the World Cup in Qatar, now the next embarrassment.
"To be honest, it's hard to find the right words. For me as a journalist, for me as a reporter, for me as a fan, for me as a German, it's a shame what we play, how we play, how we get in touch with those tournaments.
"The most embarrassing thing is how we analyse those defeats, those results, minutes after the final blow - and I'm really excited to see the consequences now."