Malaysia earned a 3-3 draw with the Koreans on Thursday after managing to cancel out Son's injury-time penalty with a 105th-minute goal.
Having already dropped points in a draw with Jordan, the Tottenham winger's team are now set to face Saudi Arabia in the last-16 - although Japan would have been their opponents had they won in Al-Wakrah.
"I would like to ask for a favour," Son told reporters post-match. "To protect the players during the tournament and just to help the team.
"It is really sad, it really hurts a lot in the dressing room.
"Some of the boys are being criticised or receiving comments that at times cross the line a little. It really hurts as a teammate. It really hurts to see these boys in pain and also getting this criticism.
"We are working very hard on the pitch. We are trying to give everything for the fans, for the country.
"Please protect the players, my teammates and the team. Before they are a player, they are a person. They have families back home, with kids."
South Korea finished a point behind Bahrain in Group E and Son said it was a wake-up call for Jurgen Klinsmann's side as they look to end a 64-year wait for a third title.
"When you go into the tournament, there are no favourites because there will always be underdogs that catch you out," Son said.
"For Asian football, it is really good that this competition is becoming even harder. Everybody is more interested in this competition now, which is a very good sign.
"It was a tough result to take but it's a big credit to the Malaysian team, they fought until the end and I was very pleased for Asian football."
Additional reporting by Reuters