The coach was alleged to have tried to slap the steward in the ill-tempered aftermath of the Serie A encounter, with the league confirming his "aggressive behaviour" in its disciplinary release on Tuesday.
However, Garcia refuses to accept the sanction, describing the judgment as an "intolerable attack" on his honour and reputation.
"Following the unfounded accusations that have been levelled against me and the subsequent sanction, I denounce this intolerable attack on my honour and my reputation," he said in a statement released via his official Twitter account.
"Throughout my career as a footballer, educator and coach I have shown exemplary behaviour that has never wavered.
"I will not accept attempts to sully my name by ascribing to me aggressive gestures that I did not commit, which I deplore and that are contrary to my upbringing.
"I will fight with every means at my disposal to defend myself against this injustice and these lies."
In addition to Garcia's punishment, Roma defender Jose Holebas will serve a one-match suspension for directing a "provocative and insulting" gesture in the direction of home fans.
The club have also been fined €20,000 for failing to co-operate with an investigation into the incident, while the behaviour of Genoa fans earned the hosts a €30,000 penalty.
