Madrid trailed to Diego Godin's opener when Ramos forced extra time with a dramatic 93rd-minute header at Estadio da Luz.
Gareth Bale put Carlo Ancelotti's side in front and further goals followed from Marcelo and Cristiano Ronaldo to seal a 4-1 victory in Lisbon.
It was Madrid's 10th European Cup - known as 'La Decima' - but their first in 12 years after a series of near misses.
The Spanish giants have since added three more Champions Leagues to their collection, but Modric is unsure whether it would have been possible if not for Ramos' famous goal.
"It's difficult to make such judgements. I don't know," he told Club del Deportista.
"It may be the case that this goal changed the history of European football. Real Madrid had already won a lot of trophies, but they hadn't lifted the Champions League trophy for 12 years.
"This goal changed something, the mentality changed. From that moment we started to be very strong in Europe and teams were afraid of us again. That shows how important mentality is in football.
"People had spent 12 years talking about La Decima and it became a mental thing. [Jose] Mourinho went to three semi-finals and it was hard to overcome this mental barrier.
"When we reached the final and to win it with that goal, it still gives me goosebumps, we showed such strong character and never gave up."
Modric broke Ronaldo and Lionel Messi's Ballon d'Or stranglehold by winning football's most prestigious individual accolade in 2018.
"That was a recognition of my entire career, but a very special year in particular," Modric said of winning the award.
"I was lucky enough to win the Champions League again, which isn't easy, and I also reached the World Cup final with a country like Croatia, which for us is something that words just can't describe.
"I don't like to talk about myself, but I think that, in the individual sense, I played a very good season and the footballing people have recognised that. It's no coincidence when so many people vote for you."