Son reached a century of Premier League goals by scoring the opener in Tottenham's 2-1 win over Brighton and Hove Albion on Saturday.
The 30-year-old is the first player from Asia to score 100 goals in the Premier League.
Son dedicated the feat to his late grandfather and hopes his exploits will help a new batch of Asian players to dream big.
"This was something that I dreamed for. It is an amazing achievement which I wouldn't have had without my team-mates," Son told BBC Sport.
"Scoring 100 goals in the Premier League is a massive thing. I was really emotional because I have had tough moments in the last few weeks.
"My grandad passed away and it was not easy. I want to send that goal to him.
"I hope all the Asian players – especially in South Korea – look at this achievement and believe they can do it as well.
"It's a good thing for Asia and I take a big responsibility to be a good example to help the young guys. I want them to believe an Asian player can do amazing things in the Premier League."
Son scored 23 goals last season to share the golden boot with Mohamed Salah but his strike against the Seagulls was just his seventh of the campaign.
"Sometimes you always expect an amazing season and think it will be the same [as last year], but there can be more pressure," Son said.
"I'm the most frustrated player but I see where I can improve. I am frustrated but I'm not the perfect player so I need to look at my weaknesses.
"The fans are supporting me and I need to take a big responsibility to do well for the rest of the season."
