Real Madrid had more "experience" than their defeated Champions League final opponents Atletico Madrid, said match-winner Cristiano Ronaldo.
The Portugal forward scored the decisive penalty in Real's 5-3 shootout win after Juanfran missed for Atletico.
The win - after the match had finished 1-1 - brought Real's 11th European title and their second in three years, coming against the same opposition.
"It is a fantastic night for us," said Ronaldo, 31.
"Our team showed more experience and we showed it by scoring all the penalties."
Zinedine Zidane's side led through Sergio Ramos' close-range finish in the first half, before substitute Yannick Ferreira Carrasco equalised for Los Rojiblancos 11 minutes from full time.
A scoreless extra time meant the match went to penalties and Atletico full-back Juanfran was the unlucky man, striking his effort against the post before Ronaldo stepped up for the winner.
"The penalties are always a lottery," said Ronaldo, who has now won the trophy three times.
'Best club in the world'
Midfielder Luka Modric picked up his second Champions League title with Real Madrid after joining from Tottenham in 2012. His total of 71 passes was the most by any Real player in the match.
"We were calm on penalties and we deserved to win," said Croatia international Modric. "I feel sorry for Atletico but I am glad for ourselves.
"This is the competition of Real Madrid, the 'undecima'. This trophy belongs to Real and that is why it is the best club in the world."