Los Blancos looked on course for a 1-0 defeat in Lisbon before Sergio Ramos took the match into extra time by equalising with seconds remaining.
"It was an unbelievable night, to win La Decima here in Portugal with a beautiful crowd," Ronaldo told Sky Sports News.
"It's something we've been wanting for many, many years and I'm really pleased and happy. I think the team deserved it because we played better than Atletico Madrid.
"I think we deserved to score four goals - we created so many chances and we had the ball all the time."
Real last lifted the Champions League back in 2002.