The South Korea and Spurs captain hinted at doubts about his international future in the immediate aftermath of a 2-0 semi-final defeat to Jordan last month.
It later emerged that the forward played with a dislocated finger as a result of a bust-up with teammate Lee Kang-in on the eve of the game.
Jurgen Klinsmann, who had promised to deliver South Korea's first Asian Cup in 64 years, was then sacked after just a year in charge.
"Playing for the national team is a promise between myself and the fans," Son told reporters following Thursday's disappointing 1-1 home draw with Thailand in a World Cup qualifier.
"I absolutely want to honour that," Yonhap News Agency quoted him as saying.
"I am going to keep my head down and play hard, and I hope I can grow into a stronger person so that I won't ever think about quitting again."
Revealing how close he came to giving up international football, Son said he had sought the advice of countryman and former Manchester United star Park Ji-sung.
"I've never once taken my spot on the national team for granted - I've felt grateful and honoured every time," added Son.
"But if I had thought only about myself, I think I would have quit."
Son scored his 45th goal for his country towards the end of the first half against Thailand, but the visitors grabbed a leveller just after the hour.
The two sides play again in Bangkok on Tuesday as South Korea close in on the next stage of World Cup qualifiers.
