Tottenham exited Europe’s elite competition at Wembley after a 2-1 defeat to Juventus.
Pochettino’s men looked to be on control of the tie when Son Heung-Min gave them the lead in the 39th minute when he scrambled home from Kieran Trippier’s cross.
But the game turned on its head in just six second half minutes when Gonzalo Higuain poked in at the far post before Paulo Dybala beat the offside trap to tuck into the net.
And Pochettino lamented the disappointing exit, insisting his side had done enough to reach the quarter-finals.
He said: “In less than three minutes we conceded two goals – two big mistakes – and that is why we are out.
“In both legs we deserved more. I feel proud. We played fantastic football until that first goal and we dominated.
“Of course we are very disappointed but it is part of growing. We will keep going. But we are very disappointed.
“We created a lot of chances. It is clear that we deserved a lot more. In football it is not about deserving, you have to score goals and not concede.
“They [Juventus] only came to our goal two or three times – not much – but they have quality so if you make a mistake they will score.”
Juventus defender Giorgio Chellini appeared to take a dig at Tottenham after the final whistle, accusing them of being mentally fragile.
He said: “It’s the history of Tottenham. They always created many chances to score so much, but at the end they miss always something to arrive at the end.
“We believe in the history. We saw it yesterday between Paris and Real, the history is important, with experience it is important, and tonight we use our skill and arrive at the win.”
Pochettino, however, thinks his side can learn a lot going forward, adding: “We played another massive team.
“For us it was tough. It was very positive for the future.
“You need this type of game and experience to build you as a player to compete at this level.”
Meanwhile, Trippier admitted his team-mates were “gutted” after the game.
He said: “We had a lot of chances in the first half and put in a great performance. It’s a difficult one to take.
“[Juventus] changed their formation and they had a lot of the ball, we just need to settle down a little bit.
“The lads are gutted because of the way we started the game. It’s a tough one to take.
“We wanted to come out fast in the second half, but they killed the tempo out of the game.”