Fenerbahce edged out Trabzonspor on goal difference after both teams finished with 82 points at the end of the season.
But senior Fenerbahce officials including the club's president Aziz Yildirim were then implicated in a match-fixing scandal.
Trabzonspor claimed Fenerbahce should be relegated as a result, with the 2010-11 title given to them instead, but CAS ruled against the club.
"There is indeed no legal provision which would have allowed TFF [the Turkish Football Federation] or FIFA to allow the second-ranked team of the Turkish Super Lig to be automatically declared champion instead of the first, if this latter is excluded," CAS said in a statement.
"Trabzonspor did not bring any evidence of the existence of legal provisions of FIFA or TFF which could serve as a basis for such a decision."