Spurs came from two goals down to draw 2-2 in the first leg in Turin, but were given a taste of their own medicine at Wembley on Wednesday.
Gonzalo Higuain and Paulo Dybala scored in the space of three second-half minutes to turn the last-16 tie around after Son Heung-min put Pochettino's men ahead before the break.
And the Tottenham boss felt slack defending proved the difference as last season's runner-up Juve moved into the quarter-finals 4-3 on aggregate.
"In less than three minutes, we concede two goals," Pochettino told BT Sport. "Two big mistakes and that's why we're out of the competition.
"At the same time, in both games, we deserved more and were the better team.
"But in football you need to score goals, more than the opponent. That's why we're out.
"I think we played fantastic football. Until we conceded the first goal, we were the better team.
"Of course, we're very disappointed but it's part of our growing."
Pochettino felt Spurs played well enough over the two legs to earn a place in the quarter-finals, although he acknowledged Juve were clinical.
"We created a lot of chances," Pochettino added. "If you compare the stats, it's clear Tottenham deserved much more.
"I think they only arrived at our goal two or three times. But they have quality and if you make a mistake, they can score.
"In the group stage, we played [Borussia] Dortmund and Real Madrid, and then against Juventus, three massive teams.
"It was tough but a fantastic experience for us. I'm disappointed for our players and our fans but it's about the future."