The ruling is the latest in a complex battle in which Sion, led by outspoken president Christian Constantin, defied FIFA and UEFA statutes by taking their case to the civil courts.
"[CAS] decided to confirm that OLA [Sion] should not be reintegrated into the UEFA Europa League 2011/12," said the Lausanne-based tribunal in a statement.
Sion had lost another key battle last month when the Valais cantonal court ruled the club could no longer field six players who were signed in the summer, when Sion were subjected to a FIFA transfer ban.
The six players had initially won a court ruling allowing them to play and, backed by this, Sion fielded them in a Europa League qualifier against Celtic, which the Swiss side won.
UEFA ruled the players to be ineligible and expelled Sion from the competition. Celtic took their place in Group I alongside Atletico Madrid, Udinese and Stade Rennes.
Sion then obtained an injunction at another court in the canton of Vaud, where UEFA has its headquarters, ordering them to be reinstated.
That injunction also said that the CAS had the jurisdiction to make a final ruling and that Sion had 60 days to file a claim, which it had not done, CAS said.
The case caused embarrassment to UEFA whose president Michel Platini was interviewed by Vaud prosecutors to explain why Sion had not been reinstated.
UEFA then drew up several possible ways of including Sion in the competition, all of which would have thrown the tournament into chaos.
The transfer ban had been imposed over a case in 2008 when Sion were found guilty of poaching an Egyptian player from his club.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.