Los Blancos sealed 'La Decima' with three extra-time goals from Gareth Bale, Marcelo and Cristiano Ronaldo against Atletico Madrid, but can be grateful for Sergio Ramos's late header for keeping them in the contest.
However, Ancelotti suggested that his team kept believing that they could turn the game around.
After the 4-1 victory, the Italian told reporters: "We thought we could tie until the last moment. We fought long and hard and it was easier after the goal.
"It is a dream come true. The happiness is very great. I dedicate this title to all my family."
For Ancelotti, it is third Champions League success, after winning the trophy with AC Milan in 2003 and 2007.
His post-match press conference in Lisbon was gate-crashed by jubilant Real players, who drowned out the Italian coach with their singing, before embracing their manager.