CAS ruled Suarez would be allowed to train with his new Barcelona team-mates and also attend games, after FIFA's original ruling saw the Uruguayan banished from all football for four months after biting Italy's Giorgio Chiellini at the World Cup in Brazil.
Suarez is also now allowed to play in friendlies, and is available for Barca's clash with Liga MX side Leon on Monday.
FrontRow Legal solicitor Richard Cramer said FIFA should internally review their processes, after appearing to make an error in their processes for punishing the former Liverpool star.
"I think it's a bit of a slap in the face for FIFA as well, it implies that FIFA have appeared to have broken their own rules, not understood their own rules," Cramer told Perform.
"This went in front of an original panel and then three or four days' later went in front of an appeals panel, both FIFA panels got it wrong, so it is a bit of a lesson to FIFA to ensure that when they're dishing out these punishments that they comply with their own rules.
"It may be that their own rules are not particularly clear, and that probably means that they will probably have to carry out an internal investigation themselves having got it so wrong.
"Actually it's quite embarrassing for FIFA because you would expect some level of consistency and the fact that CAS have come forward with a different decision to FIFA sends the message that something has gone horribly wrong with the internal disciplinary procedure."
Cramer said Barcelona had a valid legal avenue to explore in taking the Suarez case further, labelling the original FIFA punishment "Draconian".
"I think from his point of view, I think it was very important for him and for Barcelona to ensure that he could train because to actually ban somebody from any form of participation was a Draconian, capricious decision," he added.
"It didn't fit the crime because in effect you're saying to a player you can't train, you can't appear at your place of work, you can't mix with your team-mates, you can't go to a game to even watch, in my view would have been regarded as a restraint of trade."
