Griezmann confirmed on Tuesday that he intends to leave the Wanda Metropolitano at the end of the season, despite only agreeing a new five-year contract last year.
🎙 @Simeone: "We had Torres, Forlán, Agüero, Falcao, Mandzukic, Griezmann… and we always competed in the same way, because this club's structure and strength isn't like it used to be. In the last 10 years, we've seen that the club is more important than any one of us." pic.twitter.com/wFZVJJx1Di— Atlético de Madrid (@atletienglish) May 17, 2019
The France international's announcement came amid strong rumours that Barcelona are ready to trigger his release clause.
Griezmann is set to depart the club he joined from Real Sociedad in 2014, having reached double figures for LaLiga goals in all five of his seasons in the Spanish capital, scoring 94 times in total.
And Simeone says there is only so much Atletico can do to keep their star players out of the clutches of rival clubs such as Barcelona.
"First of all, I am grateful for the footballer that we've had," he said in Friday's news conference. "I only have words of gratitude for Griezmann. I love him as a person.
"I've learned not to judge the decisions of others. It's your job to have an opinion. You have to give everything without expecting anything back. When someone like Antoine gives his all for us, we're happy.
"We knew Griezmann leaving was a possibility. I spoke with Antoine before meeting with Miguel Angel [Gil, Atleti's chief executive] and Andrea [Berta, their sporting director]. I told him what I thought with affection and fondness and this was between us only.
"When you give everything, as Antoine did, we are calm. Antoine is taking a step towards a new place. We have all participated in that growth over these five wonderful years. He is one of the best scorers in our history.
"Players are always looking for important teams, like Lucas Hernandez with Bayern Munich, Barcelona... historically there are better clubs and that growth is sought."
Griezmann will join a long list of star names to have walked away from Atletico over the past decade, but Simeone insists no player is bigger than the club itself and has backed them to continue challenging for major honours in the 28-year-old's absence.
"I do not aspire to convince anyone to stay," he said. "Staying at Atletico is a source of pride for the players who do it. It's been almost 10 years since Quique [Sanchez Flores]'s time when we started competing well and winning titles.
"It was Miranda, [Radamel] Falcao, Raul [Garcia], [Diego] Forlan, [Sergio] Aguero. They went a long time ago and the club continues to be maintained, and with an absolutely better structure than in those times.
"We signed knowing that Atletico is much bigger than all of us. [Fernando] Torres, Forlan, Aguero, [Diego] Costa, Griezmann, and the club has always competed.
"The team has shown that the club is more important than all of us. It will not change anything at all. We will look for players who want to come and play for an important club like Atletico."
Atletico travel to Levante on Saturday for their final LaLiga match of the season.