The Serie A heavyweights were level at 1-1 going into the break in Cardiff thanks to Mario Mandzukic's spectacular overhead kick, but Casemiro's deflected strike, Cristiano Ronaldo's second and a late Marco Asensio effort saw Zinedine Zidane's side become the first team to retain the Champions League in its current format.
"We are disappointed," he was quoted as saying by UEFA.com.
"We played very well in the first half, we thought we had enough to win the game.
"I cannot explain why we played like we did in the second half. Real Madrid deserved to win in the second half.
"They showed their class and the attitude needed to play in this kind of game."