While Rossi lost that bid, and saw his hopes of a seventh MotoGP title disappear, the appeal with the CAS had remained ongoing, even though a ruling in his favour would have been of no practical use.
On Wednesday, the court said the 36-year-old had given up on that as well.
"Mr Rossi has now informed the CAS he does not wish to continue with his appeal," the statement said.
"Accordingly the arbitration procedure has been terminated and the FIM (International Motorcycling Federation) decision will continue to remain in force."
Rossi finished fourth in the race won by his Spanish team mate Jorge Lorenzo who took the title ahead of the Italian.
Spain's Marquez, the outgoing champion, and Dani Pedrosa finished second and third in Valencia.
Rossi, who has won 10 motorcycle world titles in all, later accused the trio of a cosy agreement to stitch up the result and ensure one Spaniard handed over the title to another.
He did not attend the prize-giving gala evening.
(Reporting by Alan Baldwin; editing by Rob Hodgetts)
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