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.
Simeone said afterwards: "Yes, it's a moment to be happy as a club, as a team, with the joy of our fans, who will celebrate this step towards the quarterfinals.
"When you get here, the road will be tough, as in previous situations where we reached the final. We'll have to compete like this; it will be difficult because we'll be facing the best attacking team in Europe, but we'll be eager to compete."
It's now eight out of 13 years in the Champions League quarterfinals and Simeone continued: "Sometimes you don't need to say anything, the numbers speak for themselves. We have to give it our all, the quality to reinvent ourselves.
"The effort was enormous. The team didn't start well, the three-goal lead didn't help. We equalized, then it was 2-1, we equalized again, we had chances to close it out, and then came the final penalty. The draw was what we deserved. I'm very happy for Cardoso, he's been working consistently, he played a high-level match, Julián, Hancko, Robin, Musso, Griezmann..."
Atlético now meet Barca in the quarters and also said: "We'll try to compete with Barcelona, who are the ones we're drawn against. I repeat, they're the best attacking team in Europe. The possibility of playing them in the quarterfinals is a high-level challenge, and it will demand that level from us."