That's because the club believes an agreement between the player and Barcelona came before July 1, when Griezmann's release clause stood at €200million.
Cerezo also hit out at Griezmann, who confirmed in May he would be leaving Atletico.
"My father taught me as a child that trains don't just pass once", he said. "It's our time. This is our path".
Atletico say they will take legal action against Griezmann and Barça in search for the additional 80 million after the player's lawyer, Sevan Karian, deposited his 120 million release clause with La Liga on Friday. His new contract includes a $900 million buyout clause.
Griezmann had been heavily linked with a move to Barca last summer but ended up signing a new contact with Atletico until 2023.
Former Atletico forward Antoine Griezmann has signed for Barcelona.
Griezmann joins Barcelona on a five-year deal with a buyout clause of €800m.
The French soccer star began his senior career in 2009 with Real Sociedad, before joining Atletico in 2014.
He won the Golden Boot at Euro 2016 when France were beaten in the final on home soil by Portugal before helping to guide his country to World Cup glory in Russian Federation past year.
Antoine Griezmann has dominated world football for the last four-five years now, holding his own in front of the indomitable duo of Lionel Messi and Cristiano Ronaldo.
The fee was a record paid by the capital city club and the highest ever received by a Portuguese outfit, and the sale of Griezmann helps finance such a huge transfer for a young player.
It was his lowest-scoring league campaign since the 2012-13 season and his lowest in Atletico colours, with Griezmann only managing 15 goals in La Liga, with 8 assists to his name.
United can nearly certainly forget about signing Griezmann now despite tracking him for the past few years.