In a statement on Tuesday, the Korean Sport and Olympic Committee (KSOC) said Kwon's actions were "extremely regretful".
"We will take appropriate measures for the situation through a comprehensive review after the Games come to an end," KSOC said.
Kwon also drew criticism from South Korea's vice minister of culture, sports and tourism, who called the player's reaction to the defeat "regretful."
Kwon apologised to Kasidit, and to his South Korean fans, in a handwritten note posted on social media.
"I behaved recklessly soon after a match ended and I shouldn't have as a national team player," he said.
Persons:
Pabellon Fuente, Korea’s Kwon, Spain’s Alejandro Davidovich Fokina, Eva Manez, Kwon, Kasidit Samrej, netizens, KSOC, Kasidit, Hyunsu Yim, Ed Davies, Peter Rutherford
Organizations:
Rights, Asian Games, Weibo, Hangzhou Olympic Sports Center, Thai, Korean Sport, Olympic, South, Thomson
Locations:
Spain, South Korea, San Luis, Valencia, Rights SEOUL, China