His side, unbeaten in 17 matches prior to kickoff and with a home victory against European champions Real Madrid under their belts this season, were heading for the last quarter-finals when Son Heung-min's first half goal put them 3-2 ahead on aggregate.
An enterprising Tottenham appeared in control but the Champions League proved an unforgiving arena.
In the 64th minute their defence fell asleep as Sami Khedira was allowed to head a cross on for the unmarked Gonzalo Higuain to tap in.
Three minutes later Higuain's pass took out the whole of Tottenham's static defence in one fell swoop and Paulo Dybala raced through alone to curl the winner past keeper Hugo Lloris.
It was a double blow that, despite a tenacious response, proved terminal to Tottenham's hopes of joining Premier League rivals Liverpool and Manchester City in the last eight.
"We made two mistakes and conceded two goals," Pochettino, who is yet to win a trophy for Spurs despite impressive progress since taking charge in 2014 said, told reporters.
"I can only say that of course Juventus is a great team; if you provide one, two chances they can score.
"We played fantastic, but we lost and now we have to think positively about the future."
Pochettino refused to blame the inexperience of his players at the highest tier of European football.
"No lack of experience, no lack of concentration," the Argentine, whose side are fourth in the Premier League after an unbeaten run stretching back to December, said.
"When you assess the game and watch it again and again, I think for more than 70 minutes Tottenham were much better and we created a lot of chances.
"We competed well against a very good team like Juve, we dominated. In the two games we were better but at this level, in three minutes, the tie was Juventus's."
Lloris, who had very little to do apart from pick the ball out of his net twice, said Juventus had shown just how tough they are, having been declared underdogs for the second leg after being outplayed by Spurs in Turin.
"They're a machine mentally," the Frenchman said. "They stayed calm and turned the match in their favour."
(Reporting by Martyn Herman, editing by Ed Osmond)
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