Griezmann announced publicly on Tuesday that he wants a new challenge following five years at Atletico, where he won a Europa League and UEFA Super Cup.
The 28-year-old's departure will be a major blow to the club, who have already lost Lucas Hernandez to Bayern Munich and face a fight to hang on to several other key players this summer.
Asked who could replace Griezmann, a smiling Simeone said at a press conference on Friday: "Someone who plays very well in three quarters of the pitch, scores 20 goals a year and is cheap. It is very difficult."
Griezmann informed Atletico of his decision in a meeting with Simeone, chief executive Miguel Angel Gil Marin and sporting director Andrea Berta.
After scoring 129 goals in 256 games for Atletico, the Frenchman is set to make his last appearance away at Levante in La Liga on Saturday.
"First of all I am grateful to him as a footballer, to the player we've had these five years and what he has given us," Simeone said.
"We cannot judge his decision, he came in one way and takes a step now towards a another goal and we have helped him grow in that time.
"He is one of the top scorers in the history of Atleti after five wonderful years. I am grateful because he has given us everything and I do not judge anything or anyone."
Despite uncertainty surrounding the futures of players like Filipe Luis, Juanfran and Rodrigo, Simeone is not concerned about a mass exodus at Atletico.
"It's been almost 10 years since the team started challenging for trophies and we have managed to do it with (Diego) Ribas, Arda (Turan), Raul (Garcia), (Radamel) Falcao, (Diego) Forlan, (Sergio) Aguero," Simeone said.
"The club always kept the very best values and the players we are looking for will have those same characteristics. You have to feel the desire and need to wear this shirt.
"It is very difficult to throw money at a player who is already a superstar. We took Griezmann from Real Sociedad and made him into a Griezmann of the future."
Rodrigo has a release clause in his contract, reportedly set at €70 million, with Manchester City among those interested in the Spanish midfielder.
"We are talking," Simeone said. "He has many things to improve, I have no doubts about his enormous potential and I am happy that big teams have watched him since his development from Villarreal.
"He feels a part of this club, he is very happy in Madrid and what we are clear on is that he is 22-years-old and he has a lot to improve.
"Today it seems like everything is changing but we have to stay calm because in many ways nothing changes."