Atletico Madrid were within 90 seconds of glory in Lisbon before Sergio Ramos' injury-time equaliser cancelled out Diego Godin's first-half effort.
Gareth Bale then gave Real the lead in extra-time before strikes from Marcelo and Ronaldo -- from the penalty spot -- wrapped the victory up.
"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.
"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 2013 Ballon d'Or winner who scored 17 goals in 13 Champions League games this season, admitted the win ranks up there among the great achievements in his 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.
"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 lauded Real manager Carlo Ancelotti, who equalled former Liverpool boss Bob Paisley's record of winning three European Cups.
"It's just amazing, he's a fantastic coach and a fantastic man so he deserves it," he said.