Tottenham Hotspur's Son was ruled out of the friendly in Busan due to injury while Napoli defender Kim was not included in the squad for the current window due to his requirement to complete mandatory military training.
The pair were among a significant number of first choice players missing from the game against the South Americans, who won thanks to an 11th minute goal from Bryan Reyna (24).
"When I don't win, I'm angry. It's normal," said Klinsmann. "But the more important thing is that we see who's growing.
"I am thankful that I get this opportunity to bring new players in and give them a chance.
"Obviously, I'd like to have Min-jae and Sonny. But overall, this is a great group of players to work with. I'm impressed with their discipline, with their work ethic and with their focus."
Klinsmann has yet to win in the three games he has helmed since taking over in February from Portugal's Paulo Bento (53), losing against Peru and Uruguay after a draw with Colombia in the German's debut in March.
The former U.S. coach reserved specific praise for 22-year-old Real Mallorca playmaker Lee Kang-in (22), who started for the sixth time for South Korea and who has recently been linked with a move to French side Paris Saint-Germain.
"His way of playing is exciting. He's always creative. He's always there trying hard, but obviously he cannot win it by himself," Klinsmann said.
"For Kang-in, this is a really important learning curve, learning when to dribble and when to just make one-touch passes to free himself up."
