Los Merengues climbed to the top of the table with an exciting victory at the Santiago Bernabeu, as goals from Gareth Bale, Jese Rodriguez and Karim Benzema, who struck twice, proved sufficient to overcome the Yellow Submarine.
Modric, whose performances have been receiving high praise recently, stressed the importance of the win as well as his gratitude for the warmth the fans have shown towards him of late.
"The victory is very important because we faced a very difficult opponent," the 28-year-old told Realmadrid TV.
"And coming off a great physical and mental effort against Atletico Madrid [a 3-0 Copa del Rey semi-final victory on Wednesday], these are three very important points.
"It's great that the Bernabeu shouted my name. I am very grateful. I'm at a good moment, as is the team. That's what matters. I'm very proud and I thank the fans."
Madrid now turn their attention to the second leg of their Copa del Rey semi final against Atleti on Tuesday and Modric insists that there is no opportunity to relax despite their comfortable lead.
"We can’t afford to be complacent, despite having a great game in the first leg," he continued.
"The tie isn't yet decided and we have to play at the Vicente Calderon as if it's 0-0. We need a goal to kill the tie."
Los Blancos now sit to of La Liga with 57 points from 23 games, level with Atleti on points and three ahead of Barcelona who play Sevilla on Sunday.