The Brazilian scored in the win to secure Madrid's 10th European Cup, their first for 12 years.
"It's an immense joy. We were slow to get it, but we know how we fought, how we sacrificed, we left everything on the field to give this joy to the fans," Marcelo told reporters.
"To those on the bench, on the pitch, in the stands, it was very nice. At last we're going to Cibeles, I'm very happy.
"There are no words. I can see it on the faces of the people, it's a huge joy. It's for everyone to enjoy, we deserved it."