Germany's 1-1 draw with the Koreans coupled with Morocco's surprise 1-0 victory over Colombia saw the European side suffer their earliest exit in Women's World Cup history.
The two-time former champions and one of the pre-tournament favorites follow Brazil, Italy and Olympic champions Canada out of the competition in double-quick time.
Colombia topped Group H despite losing and will face Jamaica in the last 16.
Morocco progressed into the knockouts on their World Cup debut also with two wins and a defeat, and meet France next. Germany were third and condemned to an early flight home.
"To be honest, it's still hard to understand," skipper Alexandra Popp, who scored the German goal and was their chief threat throughout, told German TV network ZDF.
"I still can't quite understand what happened here."
Coach Martina Voss-Tecklenburg said that there was "a lot of uncertainty today".
"In the end you have to say that our performance was not enough."
The 2003 and 2007 winners Germany came into the game in front of just under 39,000 in Brisbane knowing that a win over South Korea would put them in the last 16.
But they started badly, conceding to a smart Cho So-hyun finish after just six minutes and looking shaky at the back early on.
Colin Bell's South Korea looked nothing like the team that lost 2-0 to Colombia and 1-0 to Morocco.
Germany equalized just before half-time with a Popp header but for all their possession, last year's European finalists failed to get the second goal they desperately needed.
Popp thought she had won it in the second half with another fierce header, but it was ruled out by VAR for off-side.
Sydney Lohmann's effort went just over deep in stoppage time and Germany now needed a favour from Colombia.
A draw would have been enough for Germany had Morocco not sprung a surprise of their own in Perth.
Anissa Lahmari's goal in first-half stoppage time, after captain Ghizlane Chebbak's penalty kick was spectacularly saved, won it for Morocco.
With the Morocco game ending slightly before events in Brisbane, the Atlas Lionesses faced an anxious wait.
When Germany's fate was sealed the Moroccan players went wild on the pitch.
The Koreans finished bottom of the group with one point but at least salvaged some pride.
England now favorites?
The United States are into the knockout rounds and a date with third-ranked Sweden on Sunday, but the Americans have looked nothing like a team capable of winning a third World Cup in a row.
They scraped through with a 0-0 draw against tournament debutants Portugal, the Portuguese striking the post in injury time — a goal would have sent the U.S. home.
European champions England now look the team to beat.
They were touted before the tournament as the biggest threat to the United States and after an indifferent start, they thrashed China 6-1 to progress in style.
Sarina Wiegman's side face Nigeria, who along with South Africa, Jamaica and Morocco confounded expectations by getting out of the group stage.
South Africa scored an injury-time winner to send Italy out on Wednesday, then that same evening Jamaica strangled Brazil 0-0 to end the South Americans' hopes.
The knockout rounds begin on Saturday when an impressive Japan face Norway and Spain — thrashed 4-0 by Japan last time out — play Switzerland.
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