The Championship club claim the verdict was reached "without considering the full documentation presented by Cardiff City FC to FIFA".
Sala, Cardiff's record signing, and pilot David Ibbotson died when their Piper Malibu aircraft crashed in January. The striker had accepted a move from Ligue 1 side Nantes but the Bluebirds claimed the agreement to pay Nantes a £15 million ($18m) fee was not legally binding because conditions insisted upon by Nantes were not fulfilled.
Cardiff, who were relegated from the Premier League last season, refused to make the first scheduled payment over what chairman Mehmet Dalman identified as "anomalies" in the deal, prompting Nantes to make a complaint to FIFA which culminated in Monday's decision.
Cardiff's statement read: "Cardiff City FC is extremely disappointed at the decision of the Players' Status Committee to award against the club.
"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 FC to FIFA
"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 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.
"This is a complex matter, which includes ongoing civil and criminal considerations both in the UK and abroad, which will likely have an impact on the validity of the transfer.
"It is therefore vital that a comprehensive judgement is reached following a full assessment and review of the facts."
The €6 million Cardiff have been ordered to pay constitutes a first instalment of the overall transfer fee.
"The truth is, I don't even want that money, and I may never get it," he said.
"I don't want to make money on someone who died tragically. I'm not interested in that."
When asked why he had therefore not brought the issue to a halt, Kita replied: "I am not involved at all in the case. The lawyers are in charge of it."