The 35-year-old Croatia international was one bright spot in an otherwise disappointing campaign for Los Blancos which ended without a trophy for the first time since the 2009/2010 season.
Modric made 48 appearances across all competitions, scoring six goals and provided four assists.
"Firstly, I want to thank you for the affection and support you always show me, it makes me really happy and proud. I hope to see you all back at the stadium soon and that we can enjoy this fantastic sport all together", Modric thanked the Real Madrid fanbase in his appreciation speech.
"I don't like to talk about my performances or game, but what I can tell you is that I felt good. I enjoyed myself, played a lot and am satisfied with my performances".
He added: "The one thing I'd highlight about the team this season is the fighting spirit and resilience we showed. We never gave up in what was a really tough year for us on account of the injuries, COVID-19 and the fact that we didn't have fans in the stadium. However, we coped with all of that. Never giving up is what we've learned to do at this club, it's what this club always shows you, it's all about playing until the final whistle. That's the one thing I'd highlight".
Modric joined Real Madrid from Tottenham Hotspurs in the summer of 2012 and has won four UEFA Champions League titles, two La Liga trophies, two Copa del Reys and a host of other trophies in his time at the club.
In 2018, the former Dinamo Zagreb man also became the first player other than Cristiano Ronaldo or Lionel Messi to win the coveted Ballon D’or award in a decade.
Modric made 35 appearances and scored 5 goals in La Liga in the 2020/2021 season; the most he has managed in a single campaign in both categories since arriving at the club.