FIFPro said that the ban was excessive and that Suarez had been "trialled and vilified in public" for biting Italy defender Giorgio Chiellini during their World Cup match in June. "(That) is a long journey for a player who is already 27 years," he told reporters. "We have to have a controlled optimism because we have to respect the panel,” he added.
The 27-year-old has been banned from all football activity for four months and suspended for nine competitive internationals by FIFA following the incident which shocked audiences worldwide.
The Uruguayan Football Association (AUF) took the case to CAS, sports highest tribunal, on Suarez's behalf after losing an appeal at FIFA.
Friday's hearing was held behind closed doors at CAS headquarters in a Lausanne suburb.
"At the end of the hearing, the Panel informed the parties that it will issue its decision as soon as possible, probably before the end of next week," said CAS in a statement.
FIFPro said in a statement that "the sanctions are a disproportionate response to the offence."
"The four-month ban from all football-related activity... is unfair for Suarez as it infringes his right to work at club level," it said.
"In the international arena, where the offence was committed, a nine-match ban for Uruguay is also too strong as it effectively equates to a two-year sanction,” the statement added.
"The educative nature of the sanction mentioned by FIFA in the ruling can be much better achieved by making it partially conditional, including the obligation for Luis Suarez to receive treatment,” the statement said.
FIFPro added that Chiellini himself had called for the bans to be reduced.
"That Luis Suarez has been trialled and vilified in public, ever since the incident, is a sanction in itself," said the Dutch-based association.
"On the other hand, it has been remarkable to see the response from his fellow professionals and the victim himself, Giorgio Chiellini. Many agree the sanctions are excessive. This is an important signal for the CAS panel to consider,” it added.
Suarez, wearing a checked shirt, brushed aside photographers and refused to make any comment as he arrived by taxi. He also departed in silence.
Banned twice before for biting, he initially denied sinking his teeth into Chiellini but then apologised for the incident one week later.
The ban means that Suarez will not be able to make his Barcelona debut until the end of October and will miss the whole of next year's Copa America in Chile when Uruguay play their next competitive matches.
Uruguay will play a minimum of three and maximum of six matches at the Copa, meaning that Suarez will also miss between three and six matches of the 2018 World Cup qualifying campaign.
"The biggest issue is the nine matches because it could mean, depending on the performance of Uruguay in the Copa America, that Suarez could be prevented from playing (for Uruguay) until 2016," said Daniel Cravo, a lawyer representing the AUF.
FIFPro said that the ban was excessive and that Suarez had been "trialled and vilified in public" for biting Italy defender Giorgio Chiellini during their World Cup match in June.
"(That) is a long journey for a player who is already 27 years," he told reporters.
"We have to have a controlled optimism because we have to respect the panel,” he added.