Atletico challenged the legitimacy of Griezmann's transfer to Barcelona, alleging the LaLiga champions should have to pay the €200m release clause that was still active when they began discussions.
Griezmann would not be drawn on his former club's complaint and stated his focus was on adapting to his new team.
"I did everything as well as possible with respect to Diego Simeone, my former team-mates and Atletico Madrid to leave on good terms," he said.
"It's an issue for them. I am calm and all that matters is starting well with Barcelona, which is the most important thing.
"I heard about it [the complaint]. It's a club where I gave my all. I'm very calm. The only thing that matters to me right now is understanding the coach's tactics, getting on with my team-mates and enjoying football."
On Simeone, he added: "Our relationship was more than a coach and a player, we're like family. I got on very well with him.
"He was important for what I did on the pitch and for my private life. I owe him a lot and I love him a lot. Our relationship will carry on, even after retirement."