The Taeguk Warriors weren't the only team to drop points in Tuesday's qualifiers, with Japan also conceding a late equaliser.
The Taeguk Warriors weren't the only team to drop points in Tuesday's qualifiers, with Japan also conceding a late equaliser in their 1-1 draw with Iraq.
But after the 3-2 defeat in Doha -- South Korea's first to Qatar in 32 years -- the Korean Football Association turned on Steilike, whose team has also lost to Iran and China in Group A.
"This is a big crisis. We've lost a game which we should have won. The possibility of us surviving in the qualifying rounds is now in limbo," KFA spokesman Cho Jun-Heon told AFP.
"KFA may discuss the coach's position when it holds a meeting of its technical committee," he added.
The technical committee is due to meet as early as Thursday, with the agenda likely to be dominated by discussions over Stielike, KFA officials said.
South Korea, seeking their ninth consecutive World Cup appearance, are clinging to the second automatic qualifying spot, seven points behind already-qualified Iran and just one ahead of Uzbekistan.
"I take full responsibility for this result," said Stielike after the game. "I am the one who makes the tactical decisions."
Asked if he would consider his position, the German said it was not up to him. "I have to say this is not my decision, we have to wait and see," he said.
Steilike may not be the only managerial departure after the game as Qatar coach Jorge Fossati strongly hinted at his resignation despite the shock win.
The 2022 World Cup hosts, caught up in a diplomatic crisis after its Gulf neighbours severed ties, may also be in breach of FIFA's rules against political statements.
Players warmed up wearing T-shirts with an image of the country's emir, which has been adopted as a symbol of defiance by Qataris.
Midfielder Hasan Al-Haydos also waved one of the T-shirts as he celebrated scoring the opening goal. No immediate comment was available from FIFA.
While Qatar maintained their slim hopes of reaching Russia 2018, South Korea were dealt a further blow after striker Son Heung-Min suffered a suspected broken arm.
Korean newspapers called for Steilike to go. The Sports Chosun said the game was a "disaster" and that the last two qualifiers against Iran and Uzbekistan were "matches before the gallows".
"Stielike deceived fans. It's high time for him to leave," a Sports Seoul headline read.
Japan's campaign also took a hit when they failed to beat already-eliminated Iraq, leaving them just one point clear of Saudi Arabia and Australia at the top of Group A.
The Blue Samurai play Australia and the Saudis in their final two games in what is shaping up as a high-pressure climax to qualifying.
The top two teams from each of Asia's two groups advance directly to the 2018 World Cup, while the two third-place teams go into a play-off series.
Marcello Lippi's China also had a night to forget when an injury-time equaliser consigned them to a 2-2 draw with Syria, putting them on the verge of elimination.
The United Arab Emirates are also in deep trouble in Group B despite Ali Mabkhout's stoppage-time strike which rescued a 1-1 draw with Thailand.