The Super Lig side will be replaced in the tournament by Norwegian outfit Tromso, after losing their appeal against a ban related to match-fixing
The European game's governing body had banned the Turkish outfit from competing in Europe because of the club's involvement in a match-fixing scandal.
The Black Eagles appealed the decision and were therefore allowed to participate in the play-off round, with Slaven Bilic's men claiming a berth in the last 32 with a 3-2 aggregate success over Tromso on Thursday evening.
However, the CAS has now upheld Uefa's ruling, meaning it is the Norwegians who will progress to the group stages.
"Due to the urgency of the matter, the CAS Panel has issued its decision without the grounds," read a CAS statement. "The full, reasoned award will be issued as soon as possible.
"Uefa excluded Besiktas from the current edition of the Europa League because of match-fixing. The Turkish club appealed such decision to the CAS.
"In agreement with the parties, the CAS set a timetable for an accelerated procedure and granted the stay of the Uefa decision, allowing Besiktas to participate in the current edition of the Europa League. The parties were heard at a hearing at the CAS on 20 August 2013
"Pursuant to the Uefa decision, which is now confirmed by the CAS, Besiktas are excluded from the Europa League 2013-14."
The CAS had already upheld Uefa's decision to ban Besiktas' compatriots Fenerbahce from European competition for two years for match-fixing and it has now been confirmed that last season's Super Lig runners-up, who were beaten by Arsenal in the Champions League play-off round, will be replaced in the Europa League by Cypriots APOEL.