Sala died when his plane crashed into the English Channel on his way to Cardiff in January 2019.
But the court ruled the deal between Cardiff and Nantes had been completed before the Argentinian striker died. Sala travelled two days after it was announced he would move to the Championship.
It means the Bluebirds will now have to pay the first six million euros - a total of just over £5 million - asked for by the French side.
The full transfer fee for Sala was 17m euros (£14.5m), plus additional bonuses.
A statement issued by the court on Friday (26 August) afternoon, following the decision, read: "The Court of Arbitration for Sport (CAS) has dismissed the appeal filed by Cardiff City Football Club against Football Club de Nantes in relation to the decision issued by the bureau of the FIFA players' status committee on September 25, 2019 (the challenged decision).
"The challenged decision, in which Cardiff City FC was ordered to pay six million euros to FC Nantes in connection with the transfer of the player Emiliano Sala between the clubs, is confirmed."
Cardiff released their own statement saying: "Cardiff City is disappointed by the decision of the Court of Arbitration for Sport.
"Once the club's lawyers have digested the reasons for the decision we expect to appeal and will not be making any payments to FC Nantes in the meanwhile.
"If those appeals are unsuccessful and the club is liable to pay the transfer fee the club will take legal action against those responsible for the crash for damages to recover its losses.
"All our thoughts must continue to be with Emiliano's family, who are now supported financially by the Trust the club put in place for them."
An inquest into Sala's death, which concluded earlier this year, found he had died of head and chest injuries but would have been unconscious at the time of the crash due to carbon monoxide poisoning.
The inquest also found that pilot David Ibbotson, 59, did not have the correct licence for either a commercial flight, or one at night, and found that the aircraft itself was not operated or maintained in accordance with commercial use.
David Henderson, 67, was sentenced to 18 months in prison last November for endangering an aircraft after organising the flight.
Sala's body was found following the crash but the pilot's was not.
The court declined to hear the second part of the Cardiff's case, claiming that Nantes were liable for the crash, via their agents, and that the Welsh club are entitled to compensation.