The Turkish clubs were last month prevented from competing in Europe next season as a result of match-fixing allegations.
Fener, who had qualified for the Champions League, were excluded from competing in continental competition for three seasons in total, with the third deferred for a probationary period of five years.
Besiktas were banned from the Europa League for the 2013/14 campaign, with both clubs later announcing their intention to appeal the decision.
Those bids were heard by UEFA's Appeals Body, who confirmed today in a statement it would not be overturning the bans, although the third year of Fener's exclusion has been dropped.
The statement read: "The UEFA Appeals Body today announced its decisions following the appeals lodged by Besiktas JK and Fenerbahce SK related to the two decisions passed by the UEFA Control and Disciplinary Body (CDB) on 21 and 22 June 2013, respectively.
"The UEFA Appeals Body carefully analysed the statements and documents submitted by Besiktas JK and Fenerbahce SK related to their specific cases, as well as the statements and documents submitted by the UEFA Disciplinary Inspectors appointed to each case, and reached the following decisions:
:: Besiktas JK has had their appeal rejected. Consequently, Besiktas JK is not eligible to participate in the 2013/14 UEFA Europa League.
:: Fenerbahce SK has had their appeal partially admitted. Consequently, Fenerbahce SK is excluded from participating in the next two UEFA club competitions for which they would qualify, including the 2013/14 UEFA Champions League."
UEFA added that both clubs can still appeal to the Court of Arbitration for Sport.
Fener, who reached the semi-finals of the Europa League last season, finished second to Galatasaray in the Turkish Super Lig, one place above Besiktas.