Kerr had her first chance in the fourth minute, forcing Kim Jung Mi to pull out a diving save.
She had another excellent opportunity when she was played through by a clever Kyah Simon pass only to collide with the goalkeeper and go to ground. The referee consulted VAR before deciding not to award a penalty.
Kerr came closest in the 20th minute when, from a corner, she rose to thump a powerful header against the post.
The South Koreans began to grow in confidence while the Australians lacked the incisiveness they had in the opening minutes.
The boot was on the other foot after the restart and the Matildas had goalkeeper Lydia Williams to thank for keeping them in the game in the first 10 minutes of the second half.
She stood up big and narrowed the angle to block a shot from Geum-min when the forward was through on goal in the 50th minutes. Five minutes later she dived to palm away a header from So-hyun when the midfielder was left unmarked in the area.
The Australians thought they had a shout for a penalty on the hour mark when Steph Catley was impeded, but it was ignored.
Kerr spurned a glorious chance to break the deadlock 15 minutes from time when she was presented with an open goal only to send her shot wide.
It was to prove costly when So-yun blasted home the late winner.
Gustavsson took full responsibility for the tournament disaster and acknowledged that there will now be calls for his sacking.
“I have been around long enough to know those questions are going to come from all over the place, and that’s fair, it’s OK. That’s what it should be in this business, and it’s not for me to decide,” he said when asked if he thought he would keep his job.
“It’s not my job to say. What I can promise is that I have been around long enough to come back from a situation like this and learn from it and do better and that’s what I am going to do if I get the chance to do it.
“I know the pressure is going to be on me and I take full ownership of the result tonight. I am happy for them to criticise me, which is fair, but do it by looking at the performance as well, so it is fair criticism.”
Gustavsson exonerated Kerr, who missed a number of chances, from blame, declaring her “the best person ever”.
“She started to apologise for missing chances. I told her, ‘You don’t need to apologise, Sam.’ Sam is a rock star, she is our captain, she always carries the team on her shoulders,” he said.
“She is going to try to take responsibility for this loss, but it is not her fault, it’s a team performance. Sam is a phenomenal player. This is not about Sam, it’s about us losing a game, and if someone should be criticised it’s me, not Sam.”
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