After securing a comeback 2-2 draw in their last-16 first-leg tie in Turin, Spurs took the lead at Wembley through Son's 39th-minute goal.
However, Juve hit back with two goals in just three minutes in the second half to seal a 2-1 win on the night and a 4-3 aggregate victory over Tottenham to book their place in the Champions League quarter-finals.
Son was left visibly devastated at the full-time result and, after the game, he displayed his "sad" emotions in a television interview in which he insisted Tottenham should have beaten Juventus.
"[We are] sad...everyone is disappointed," Son told beIN Sports. "I think we deserved more than this. We dominated the game. We had lots of chances to score.
"I feel just sad."
When asked if he was hurting more knowing that Juve scored with two of their three on-target chances at goal at Wembley, Son replied: "You know what? It's football.
"Sometimes you score goals, and concede a goal. But we dominated the game from the start. In the first half we had lots of chances to score. And they scored two goals in, I don't know, five minutes.
"We need to accept the result but I think we deserved more than this."
When it was put to Son that Spurs may have lost concentration in the second half, which resulted in Juve's goals, he said: "No, I don't think so.
"We played very well, we played constantly from the start until the end. But sometimes football [there are] mistakes. But we need to go again.
"Of course, it's sad news. It hurts a lot, but we need to go again."
When then asked what he had learned from the defeat, Son said: "I'm still a young player. I learned something again today. Football is for 90 minutes, not just the first half.
"We need to be focused from the start, and we must learn something from here."