The Koreans take on Saudi Arabia in the last 16 on Tuesday with a toxic atmosphere threatening to envelop the team after a shaky start to their bid for a first Asian title in 64 years.
An opening 3-1 win over Bahrain in Qatar was followed by a 2-2 draw with Jordan that saw Klinsmann's side need an injury-time own goal to salvage a point.
Worse was to come when they conceded a last-gasp equaliser in a 3-3 draw with Malaysia - ranked 130th in the world - to finish as runners-up in Group E behind Bahrain.
Tottenham star Son said after the game that "comments that cross the line" had been aimed at his team-mates.
"It really hurts as a teammate to see the boys in pain," said Son.
Striker Cho Gue-sung and left-back Lee Ki-je have come in for particular criticism, with Cho missing a string of chances in three goalless appearances.
The 26-year-old gained huge popularity among South Korean female fans following the 2022 World Cup and the Denmark-based attacker has appeared in celebrity television shows.
Now he is accused of not concentrating on football and his Instagram account has been flooded with hundreds of critical comments.
But fans and media have reserved their strongest ire for the German legend Klinsmann, who could be seen grinning on the bench after Malaysia scored their 105th-minute equaliser.
"It was a day of shame for Korean football," the JoongAng Ilbo newspaper said on Friday of the draw with a team that was already eliminated.
A World Cup winner as a player, Klinsmann has faced heavy criticism ever since taking charge a year ago.
His refusal to live in South Korea has been a major bone of contention, as have his tactics, team selections and previous managerial record.
As a coach he is best known for managing the United States in 2011-2016.
Before South Korea came calling, his previous job was a 10-week stint at Hertha Berlin in 2019-2020.
Grin and bear it
Freelance football writer Hong Jae-min, who is covering the team in Qatar, said some Korean fans view Klinsmann with "hatred".
"Korean football fans don't like him and don't support him," he told AFP.
"Klinsmann is always smiling. Even after he lost, or he drew against Malaysia - they conceded three goals and he still smiled."
The JoongAng Ilbo newspaper said: "He sat on the bench throughout the game and just smiled."
Klinsmann admitted to being "a little bit angry" after the Malaysia game but he has remained relentlessly upbeat throughout the tournament.
His sunny demeanour stands out even more when he is in the presence of stern-faced assistant Cha Du-ri, who often stalks the touchline barking instructions to the players.
Klinsmann told reporters after the Malaysia game that he saw "a lot of positives".
"It was actually really OK apart from those two goals," the 59-year-old said.
"It is what it is."
'Chaotic'
South Korea now face a stern test in the last 16 against Roberto Mancini's Saudi Arabia.
Klinsmann has been helped by the return of Wolverhampton Wanderers forward Hwang Hee-chan, who missed the first two games with injury but came on as a substitute against Malaysia.
Klinsmann also has an in-form player in Paris Saint-Germain's Lee Kang-in, who has scored three goals in Qatar and emerged as one of South Korea's key players.
In Son, they have Asia's best player.
But the coach's optimistic outlook is not shared by the journalist Hong, who said the team's last two performances in particular have been "chaotic".
"Football fans in Korea think we are lacking leadership from Klinsmann," he said.
"In any match you need to show some positive movement, positive build-up or how to break down defensive teams.
"The Korean team at this Asian Cup hasn't shown any of those things."
