The world governing body this week ordered Cardiff to pay French club Nantes an initial six million euros ($6.5 million) in their dispute over the payment of the transfer fee for Sala.
The amount corresponds to the first instalment of the 17 million-euro fee Cardiff had agreed to pay Nantes before the Argentine, 28, died in a plane crash in January while travelling to join his new club.
The Championship club, who argue that Sala's revised contract was not signed and that his playing registration was not complete, said they were "extremely disappointed" by the FIFA Players' Status Committee's decision.
"It would appear the committee has reached its conclusion on a narrow aspect of the overall dispute, without considering the full documentation presented by Cardiff City to FIFA," the statement said.
"Nevertheless there remains clear evidence that the transfer agreement was never completed in accordance with multiple contractual requirements which were requested by Nantes, thereby rendering it null and void.
"We shall be appealing to CAS (Court of Arbitration for Sport) in order to seek a decision which considers all of the relevant contractual information and provides clarity on the full legal situation between our two clubs."
In a statement on Monday, FIFA said it had "never lost sight of the specific and unique circumstances of this tragic situation during its deliberations on the dispute at stake."
Nantes said they were pleased with FIFA's decision.
"Cardiff must honour their commitments and the rule of the laws of sport," the club's lawyers wrote in a text message sent to AFP.
Nantes had previously appealed in February over Cardiff's failure to pay the 17 million euros they said was owed because Sala had already signed for the Welsh side.
The light aircraft Sala was travelling on came down in the English Channel during a night-time flight.
His body was recovered, but that of the pilot, David Ibbotson, has never been found.
A report by Britain's Air Accidents Investigation Branch in August said that Sala and the pilot were likely exposed to "potentially fatal" levels of carbon monoxide on the plane.
In the aftermath of the tragedy, Cardiff were relegated from the Premier League after just one season back in the top flight.