Griezmann announced his retirement from Les Bleus last month after being their most important player for a decade, helping them win the 2018 World Cup and finish as runners-up in 2022.
Despite Griezmann's pivotal role in the French team, the captain's armband was given to striker Kylian Mbappe ahead of him. Mbappe was booed during Real Madrid's shock 1-0 Champions League defeat by Lille earlier this month for opting not to play during the international break.
Atleti host French side Lille on Wednesday, following a humiliating 4-0 loss at Benfica in their last Champions League game and a 2-1 home win against German side RB Leipzig in their opener.
"I believe Antoine has given all his talent, his game, and leadership to France. He has won titles, developed a playing style that has progressed (the French team), and gave it all for his country until the day he retired as a standout player," Simeone told a news conference.
"The same has happened with us, and he is an extremely important player for us. He won’t have these national games that usually add significant strain to his legs after so much playing time, and we hope we can continue to enjoy all the potential he has."
Atleti have scored two goals in their last two Champions League games, despite bolstering their attack with forwards Alexander Sorloth and Julian Alvarez and midfielder Conor Gallagher in the close season.
"Julian is improving every day, settling into the team and the new city," Simeone said of the former Manchester City player, who has scored three goals in 12 appearances for Atleti.
"He's starting to show all the unique qualities he possesses. I have no doubt that he will make a difference."
Atleti will be without defender Robin Le Normand, who suffered a traumatic brain injury during their 1-1 draw in the Madrid derby last month as well as midfielders Marcos Llorente, Pablo Barrios and defender Clement Lenglet.
Atletico Madrid have decided not to sell tickets to some of their supporters for their next five away games in all competitions after sanctions from UEFA and the Spanish football federation (RFEF), this includes their next Champions League fixtures at Paris St Germain and Sparta Prague.