Son slept through Spurs' 3-0 win over Manchester United on Monday night having earlier played all 120 minutes of South Korea's 4-3 extra-time win over Uzbekistan.
"It was too late, it was two o'clock in the morning here so I was sleeping but I was very happy when I saw the result," the 26-year-old said.
"I was very happy for that and very proud of my team mates. I'm here but I'm still watching my team mates, so I was very happy."
Son made one appearance from the bench for Spurs before linking up with South Korea's Asian Games squad earlier this month. Spurs are currently second in the Premier League, behind Liverpool on goal difference, after winning all three of their opening fixtures.
He will not return to Tottenham until the middle of September as he is set to join up with the senior national side next week for friendlies against Costa Rica and Chile and he knows he may have to bide his team to reclaim a place in Mauricio Pochettino's starting line-up.
"I've missed already three or four weeks and we have the international break before I will be back," he said.
"I'm ready for that. Even when I don't play I will be waiting for my chance. We're one team and I have to be ready to play for my team."
Despite his exertions for his country in sweltering Indonesian conditions, Son said he would be in good shape for the restart to the domestic season
"Of course, it's a bit different with the weather and the humidity, and the pitches are also different, but I'll be ready when I go back to Tottenham," he added.
All that stands between South Korea and the gold medal is a win over fierce rivals Japan and while Son was reluctant to talk too much about the prospect of winning a military exemption he was in no doubt as to the importance of rounding out the tournament with the victory.
All able-bodied South Korean men must complete 21 months service in the military as a deterrent against the North, but exemptions are offered to athletes who win gold at the Asian Games or a medal of any colour at the Olympics.
"It's a final," said Son after the Koreans defeated Vietnam 3-1 to advance to the final on Wednesday.
"I can't say anything but it's very important. We're already here in the final to win something, not just coming to the final just to play it.
"Korea wants to win and I think we deserve to win.
"We're strong enough mentally, physically. We can beat any team in the final."
(Editing by Peter Rutherford)
