Zinedine Zidane's Madrid continued their stranglehold on the Champions League with a 3-1 win over Liverpool in Saturday's final in Kiev, where Reds goalkeeper Loris Karius made two key errors.
Gareth Bale came off the bench and scored twice - including a stunning overhead kick - as Spanish giants Madrid became the first team to claim three successive titles in Europe's top-tier competition since Bayern Munich between 1974 and 1976.
And Croatia midfielder Modric likened Madrid's achievements to historic basketball franchises the Bulls, Celtics and Lakers.
The Bulls twice won three straight titles between 1991-1993 and 1996-1998, the Celtics won eight in a row from 1959 to 1966, and the Lakers won four titles in five years during the 1950s, while they also dominated the NBA in the 1990s and early 2000s.
"It's something unbelievable, it's something historic," Modric told BT Sport. "I don't know if anyone will repeat this in the future. It will be very difficult
"Twice was something amazing but this is heroics. We watched a movie yesterday about basketball teams like Chicago Bulls, Boston Celtics and Los Angeles Lakers.
"When they won it three times in a row and they called it a dynasty. I think this it is a dynasty in football
"We are champions and we need to enjoy this."
Modric, whose Madrid claimed a 13th trophy in the tournament, added: "Every title is special. The first one was after a wait of 12 or 13 years to win it for Real Madrid. Every trophy is special.
"This one, third in a row. I don't think anyone will repeat this.
"We have to enjoy it firstly and then prepare for next season and go for a fourth in a row."