Late goals from Dani Carvajal and Vinicius Jr saw Real win 2-0 at Wembley against Borussia Dortmund.
Florentino later said: "It's a magnificent night because this competition is the one we like the most. Santiago Bernabu created it and it made us important on a global scale. Every time we win it, there is satisfaction among the players, the president and all the fans around the world.
"Borussia are a great team and I am a good friend of their CEO, who sold Bellingham to us. At the beginning it was a difficult game, in the first half we didn't play too well. Then in the second half we got into the game but we all knew we were going to win and that it was only a matter of time before we got the goals.
"Two years ago the same thing happened and we always go for every trophy. Sometimes we win and sometimes we don't. The Champions League has a very special motivational factor because it transcends the national level and also because it is followed by billions of madridistas all over the world."
He also said: "We are going to keep working hard to ensure that next year the fans can celebrate again. What we have achieved is not easy. The love affair between Real Madrid and the Champions League is a special motivation for everyone. What we have achieved is not easy, but for us it is easier than for others.
"Madrid are a team used to winning. It is part of our history and our DNA and my job is to continue to motivate the players so that this history continues and will last forever."