Atletico had beaten Chelsea, Barcelona and AC Milan to reach the final, however.
"I've learned that every team can win the Champions League if you put your mind to it," Alderweireld told reporters.
"If you have a good squad and the hunger is there to win something, you can do it.
"At Atletico, we had the big teams like Barcelona, Real, Bayern Munich - they were always the favourites. But at Atletico, if you are a really good group and, of course, we had quality too, you can win it.
"That's the thing that has stayed with me."
Spurs lost their Group E opener to Monaco at Wembley Stadium earlier this month, but Alderweireld is confident they can cope with the pressure when they face Russian side CSKA Moscow on Tuesday.
"We know that there is a little bit more pressure because we lost the first home game but we have to have confidence in our own game and try to give everything on the pitch," the Belgium international added.
(Reporting by Ian Rodricks in Bengaluru, editing by Nick Mulvenney)
