The lawyer for the country's governing body admits they hoped to see the striker's suspension reduced, while Fifpro have voiced their support for the player
The striker was banned by Fifa for nine competitive Uruguay matches after he bit Giorgio Chiellini during the Celeste's 1-0 World Cup win over Italy in June, as well as being suspended from all football-related activity for four months.
The international ban was upheld by CAS on Thursday, despite the non-playing portion of the punishment being lifted, leaving the AUF fuming.
"We are enormously frustrated because we understand that, with the behaviour of Suarez in that match he of course deserved to be punished, but we don't think that it was the worst behaviour of any player at a World Cup," Daniel Cravo, the AUF's lawyer, told Sky Sports.
"We considered that the situations he was involved in in the Netherlands and England could not be taken into consideration," he added, referring to previous biting incidents when playing for Ajax and Liverpool. "But, of course, we respect CAS' decision, we wait to see what the grounds are, and we are sorry for not achieving what our client wanted from us."
Suarez has received further support from the world footballers' union, Fifpro.
"Fifpro wants to express its disappointment with the decision,” it said in a statement. "Fifpro – the voice of all professional footballers worldwide – remains of the view that the current sanctions are disproportionate in relation to his violation of the Fifa Disciplinary Code.
"Fifpro does welcome the fact that CAS has cancelled the four-month ban from all football-related activity, which was unfair to Suarez as it infringed his right to work at club level.
"Fifpro regrets that CAS has not decided to reduce the length of both playing bans in exchange for an obligation for Suarez to receive treatment."
The 27-year-old is finally set to be unveiled by new club Barcelona on Monday following the lifting of the non-playing ban, and he could feature in that night's friendly clash with Club Leon at Camp Nou.