Trailing 1-0 from the first leg in London, Spurs fell 2-0 behind at half-time, but a second-half Lucas Moura hat-trick, including a 96th-minute winner, sends Spurs to Madrid to face Liverpool in the final on June 1.
Speaking to BT Sport after the game, Pochettino could not keep back his tears, as he had on the pitch after full-time, and thanked football for giving him this moment.
“It’s still difficult to talk, the emotion is amazing,” he said. “Thank you football, thank you these guys, these players are my heroes. I told you in the last year, I told everyone that we have a group of players who are heroes. They showed today. The second half was amazing.
“Thank you. Thank you football. Thank you to our fans. Thank you to the people who believed and helped us achieve this amazing moment. It’s difficult to describe.
“The game against Man City [quarter-final] and today, it’s amazing. I am so grateful to be a coach. To have a chance to play in this final is amazing. For my family. It’s amazing to award them.”