Griezmann left the club for Barcelona just over a week ago, a move that upset many at the Wanda Metropolitano.
Atletico claim the LaLiga champions still owe an additional €80million, believing Barca to have privately agreed terms with the France international before his release clause dropped from €200m to €120m on July 1.
The sense of resentment is not shared by Rojiblancos boss Simeone, who holds no ill will towards the player he signed from Real Sociedad in 2014.
"I talked with him a lot," Simeone told TyC Sports. "It's an important moment in his career in which he decided to move to an extraordinary team like Barcelona.
"I am grateful to the people who have been with us. People are normally valued for the final decision, but not by me. I value the five years he gave us that were faultless.
"He gave his best, he improved as a player and he listened to us. He makes me happy as a coach.
"I love him very much and I have a great relationship with the family.
"Obviously he's going to a very strong team and surely if he maintains the rhythm of when he was among the best he will have a great season."
Griezmann won the Europa League and secured two third-place finishes in the Ballon d'Or under Simeone's guidance.
The mutual respect between the pair has shone through amid the tension between Griezmann and his former employers.
"I am lucky to have learned from Cholo Simeone," the World Cup winner said in the wake of his move to Barca.