Sala's plane crashed in the English Channel, killing him as well as the pilot, as the Argentine striker travelled to Cardiff after signing for 17 million euros ($18.71 million) from the Ligue 1 side in January 2019.
Cardiff were told by FIFA to pay the first instalment of the transfer fee agreed before Sala's death, which amounted to six million euros ($6.60 million), and they were placed under a transfer embargo in December after failing to pay the amount.
After Cardiff's appeal at the CAS failed, they paid the amount after which FIFA lifted the embargo but the Welsh club then went to the Swiss Federal Tribunal.
"The Swiss Federal Tribunal has decided that the Court of Arbitration in Sport doesn't have jurisdiction to deal with Cardiff City's claim for damages against FC Nantes," the Welsh club said in a statement.
"This isn't a surprise and the club has already prepared separate legal action against them which will be started straightaway as FC Nantes must be held responsible for the accident (sic) (plane that crashed which was) organised by their agent.
"This will be to recover what the club paid for Emiliano and additional damages for further consequential losses."
Cardiff were relegated at the end of the 2018-19 season after finishing 18th and have not gained promotion back to the top flight since.
