The Uruguay international, who was found guilty of biting Giorgio Chiellini in his side’s World Cup group game against Italy in June, has been banned from all footballing activity, including training and attending stadiums, for four months.
However, Gaspart believes the punishment is too severe and will unfairly hinder Barcelona, Suarez’s new club, after he made a reported €95 million [£75m] move to the Spanish giants from Liverpool recently.
"The officials at Fifa have to realise that they cannot blame the club for something that happened [before Suarez was signed], whether it was accidental or not accidental," Gaspart told Sport.es.
“I think it is unfair to punish the player so severely as it is also punishing the club greatly and this isn’t fair on Barcelona.
"What has the club done to not be able to present the player? What has the player done so that he is unable to play for Barca? Nothing.
“For this reason, I hope Fifa reconsider the sanction and find another punishment that will not disadvantage the club. There is no blame on Barca, all they have done is sign a great player who they legitimately paid for."