Victory, which came from a last minute penalty from Xavi Simons, wasn't enough for Spurs as Atletico reached the Champions League quarterfinals 7-5 on aggregate.
Simons scored twice and was named man-of-the-match on the night. He later said: "In the first half especially, I really enjoyed seeing how we played.
"We wanted to win, and achieved that. It was not enough but we have to go on. Playing in the Champions League is my dream, being on the biggest stage, and whenever I put this shirt on I want to give my best. Today I enjoyed it.
"Pushing Atleti all the way is something to be proud of. Obviously we wanted to go through and play the next round, but you have to try to take the positives.
"We know where we are at the moment and we just have to stick together and make the fans proud."