Madrid were within two minutes of going home empty-handed but were saved by Sergio Ramos' injury-time headed equaliser, a goal which took the game to extra-time where goals from Gareth Bale, Marcelo and Ronaldo - from the penalty spot - gave the Spanish giants their long-awaited triumph.
"It was an unbelievable night, to win La Decima [the club's 10th European title] 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 always believed, but we know that to score in 92 minutes is a lucky moment but when you force the game all the time and you believe, it's always more easy.
"I think we deserved to score four goals - we created so many chances and we had the ball all the time."
Ronaldo, the reigning world footballer of the year, said the achievement may qualify as the best of his illustrious career.
"Every year I try to do my best, I score goals and I help the team - but maybe because we won the Copa del Rey, we won the Champions League and I won the golden boot," added Ronaldo, who scored 17 goals in 13 Champions League games this season.
"Of course it's a dream for me.
"I'm really proud to win it here [in Lisbon, where he started his career with Sporting]. We've worked all these years to win these kind of trophies so I'm happy with my team-mates and the fans - they deserve that."
Ronaldo also paid tribute to manager Carlo Ancelotti, who followed legendary Liverpool boss Bob Paisley into the record books as the only coaches to lift the trophy three times.
"It's just amazing, he's a fantastic coach and a fantastic man so he deserves it," he said.