Lee bowed down to offer a formal public apology at Seoul World Cup Stadium after being called for South Korea's home-and-away World Cup qualifying fixtures against Thailand.
Son was left with a dislocated finger as the teammates got into a scuffle on the eve of their Asian Cup semi-final.
Lee had received heavy criticism in South Korea, where Tottenham Hotspur forward Son remains the most popular athlete.
The Koreans ended up losing the semi-final to Jordan, a result which extended their 64-year wait for a third Asian title and also led to coach Jurgen Klinsmann being fired.
"I received so much love and support from fans during the Asian Cup, but I did not reward my fans and I disappointed them," Lee told Korean media on Wednesday.
"Criticism from everyone will help me down the road. I will try hard to become a better person and a better football player, someone who can help the team and set good examples."
Earlier in the day, Son told a press conference that Lee had also offered "a heartfelt apology" during Tuesday's team dinner and the squad had fully accepted it.
"It takes courage to apologise, and Kang-In stood in front of everyone to do it sincerely," Son said.
"I think it allowed everyone to really come close. The vibe in the room is not too bad. I think you won't have to write about my finger anymore."
