The South Korea international opened the scoring on the night, but his side suffered a 2-1 loss to bow out 4-3 on aggregate in the last 16.
It ended Tottenham's run in Europe after two wins over Borussia Dortmund and a victory over Madrid in group stage had the club looking like a contender.
However, Son said those results were irrelevant after Spurs exited the Champions League, with the 25-year-old feeling his side were unlucky to be out of the competition.
"It doesn't matter when we beat Real Madrid or Dortmund, it doesn't matter," he said.
"Juventus is another good team, and another top team in Europe. I think we played very well – better than them.
"I say we deserved more than this but football is about scoring goals and they scored two goals at Wembley Stadium. We have to accept the result."
Goals from Gonzalo Higuain and Paulo Dybala in a three-minute span saw Juve complete a stunning second-half comeback at Wembley, with Spurs unable to respond.
And Son believes luck played a large part in Juventus moving forward.
"Our performance was very good and I think we deserved more than this," he continued.
"The last Harry [Kane] header ... if we're lucky then that's going in... we should have got a penalty I think.
"But as I said, they scored two goals. Football is about scoring goals, and if you don't score, you lose of course.
"But I think we're unluckily out of the Champions League."
Tottenham must now turn their full focus to the Premier League, where they hold a five-point lead over fifth placed Chelsea, and the FA Cup, where the London outfit face a quarter-final against Swansea.