The Is Arenas failed security checks which led to the game being cancelled after Cellino insisted on inviting season ticket holders to the game.
"Cellino's behaviour is unacceptable and even damages the image of Italian football abroad," said Federation President Abete.
"This whole affair started off almost like a joke with Cellino saying this summer he had four stadiums to choose from, then we ended up like this.
"It is incredible, unacceptable and disconcerting. Cellino represents the Lega in the Federal counsel, so he is to be considered one of the most representative figures in Serie A and that requires a sense of responsibility too.
"Instead, this was an open challenge to the authorities in charge of public safety. All of this will certainly be punished, but the Lega has to learn from it and try to improve the behaviour of its directors."