Griezmann completed his €120million move to Barca last week after spending five years at Atleti playing under Simeone.
His exit left a sour taste in Madrid, with Atletico adamant they should have been paid €200m because they say Griezmann and his new club agreed terms before July 1, when his release clause dropped by €80m.
Barcelona are confident there is "no evidence" of such an agreement taking place and, despite the bad blood between the two clubs, Griezmann has spoken glowingly about Simeone.
"I am lucky to have learned from Cholo Simeone. Thanks to him, I've been playing at a very high level," Griezmann said in an interview with Barcelona.
"At Atletico, there's never a day off. It's very physical and there's a lot of hard work on tactics. Nobody can let their guard down."
Griezmann won a Europa League, Super Cup and Supercopa de Espana at Atleti, but the France international ended up on the losing side in the 2016 Champions League final.
Cross-city rivals Real Madrid emerged victorious in a penalty shoot-out after Griezmann had hit the crossbar with a spot-kick in normal time.
"I know that if I win a Champions League with Barca, it won't make up for the pain of losing that final with Atletico," Griezmann added.
"For the fans, for my team-mates, that was a tough moment."