Los Blancos became the first team in the Champions League era to win back-to-back titles as they swept aside Juventus in Saturday's final in Cardiff.
"All we can keep doing is keep working hard and hopefully there will be more to come".
"The first half was really tough, against a brilliant team in every aspect, but in the second half we saw the best performance from Real Madrid all season", he said. "He knows that we are a very good team and that is why we proved it in the second half".
But Casemiro restored Madrid's lead just beyond the hour and further strikes from Ronaldo and substitute Marco Asensio sealed victory for Zinedine Zidane's side, European champions in three of the last four seasons.
"Two Champions Leagues in a row".
United spent the season in the Europa League because they failed to qualify for the Champions League and, by finishing sixth in the Premier League this year, would have missed out again but for the Europa League win against Ajax and Stockholm.
Casemiro made it 2-1 after 61 minutes when his defelcted long-range wrong-footed veteran keeper Gianluigi Buffon - who has now lost in three finals - and Ronaldo swept in the third at the near post after a great run and cross by Luka Modric.
It was the only high point for Juventus on a night when the Italian champion was outclassed in its quest for a first European title in 21 years.
"We won a double that will be in history". He has a reputation for ushering in Real Madrid's pursuit of Galacticos. "We had to try to score a goal, get ahead, and then defend in the second part of the game".
After taking the lead through Ronaldo, Madrid were rocked back on their heels by Mario Mandzukic's stunning overhead kick equaliser before the interval.
Leonardo Bonucci's raking pass was volleyed into the box by Alex Sandro and Gonzalo Higuain kept the ball airborne for Mandzukic to chest it up and send a looping volley over Keylor Navas.
In his 17 months on the bench at the Estadio Santiago Bernabeu, Zidane has seen Real lift two Champions Leagues, a LaLiga, a UEFA Super Cup and a Club World Cup.
There have been 74 scorers who have contributed to their tally over the 25 years it has taken them to reach this mark, and here are the men who have weighed in most heavily. He told me sometimes I was going to play more defensive and in other games he was going to need me more forward.