Son, 30, finished as the joint-top scorer in the Premier League with 23 goals to help Spurs finish fourth under Conte last season, but the South Korea international has scored only six times in the league so far.
Tottenham parted ways with Conte on Sunday, eight days after he blasted his players as selfish, lacking team spirit and unable to play under pressure in an extraordinary media conference following a 3-3 draw at Southampton.
“As a player, I am really sorry. He’s a world-class coach, and we had a great journey together,” Son said after South Korea’s 2-1 friendly loss to Uruguay in Seoul on Tuesday.
“I should have played better. I feel responsible for his departure, because I haven’t helped the club all that much.
“I am grateful for what he’s done … He’s such a great coach and has so much experience. I will be rooting for him.”
Tottenham have been eliminated from the domestic cup competitions as well as the Champions League. They are fourth in the Premier League with 49 points from 28 games and return to action at Everton on Tuesday.