UEFA judged that Fenerbahce officials fixed matches to win the 2011 Turkish league, and Besiktas fixed its 2011 Turkish Cup victory.
Fenerbahce has sent UEFA a letter on behalf of its players, protesting what is now its second Champions League ban within three seasons.
Forward Dirk Kuyt wrote that players had "a lot of questions" for UEFA, according to a statement published by the Istanbul club.
"It's very hard to understand after a one-year ban from European competitions in the season 2011-2012," said Kuyt, a Netherlands international, who helped Fenerbahce reach the Europa League semifinals last season.
"This is not even proven that we are guilty. The next year we are allowed to play football in Europe. But after that UEFA comes back again with a higher punishment," Kuyt said
UEFA rules bar clubs from its competitions for one season if they are connected to fixing matches played since April 2007.
UEFA's latest ruling also barred Fenerbahce for an additional season of European competition when it next qualifies.
Besiktas qualified for the Europa League by finishing third in the Turkish league, but could enter the Champions League in place of runner-up Fenerbahce.
Galatasaray, the historical rival of Fenerbahce, won the Turkish league and will play in the elite Champions League group stage, which starts in September.