Spurs booked their unlikely place in the knockout stages with a draw against Group B winners Barcelona, thanks to Lucas Moura's late goal in the Nou Camp.
They were heading out of the competition as they trailed to Ousmane Demebele's opener and Inter Milan, whose result Spurs had to match, were drawing against PSV Eindhoven, until their late rescue act.
Pochettino's side looked dead and buried at the halfway point of the group stage as they had just a point from three games, appearing to kill the prospect of playing in the premier European club competition at their new stadium.
Now, having taken seven points from their final three games, Spurs should get that chance when the competition resumes after Christmas, with the Premier League club hoping to move into their new home in January or February.
The Spurs boss said: "I am so happy, so proud, I think people said it was mission impossible but we are here and we are in the next stage, it is a massive achievement for the club, we are so happy for the fans.
"It is a massive boost for the club, to have the idea to play the next stage in the new stadium is a massive motivation for us. Of course it is great for the club, a massive achievement for the club.
"The possibility of playing Champions League football in our new stadium will be a big boost for everyone. It's so important for the club and the players, but for me it is always about to win and now we are happy and are going to enjoy a little bit."