The Ivory Coast international was seen ducking for cover and shielding his face with his hands as he was showered by a series of missiles while attempting to take a throw-in in the match that ended in a goalless draw.
"The treatment Emmanuel Eboue was given by Besiktas fans on Sunday has nothing to do with racism," Besiktas spokesman Mete Duren said on Monday.
"Similar treatment was given to a Turkish player during the game as well, the sole motivation for the act was Eboue's theatrics aimed at deceiving the referee."
Home fans reacted angrily as they felt the former Arsenal player had over-reacted to a tackle and had dived to mislead the referee.
Sunday's incident follows the outrage caused by FIFA president Sepp Blatter last Wednesday when he suggested incidents of racist abuse on the pitch should be settled with a handshake after the game.
The comments drew criticism from many, including Eboue who wrote on his Twitter account "say #NO2RACISM", and forced Blatter to apologise just two days later as he reiterated the governing body's "zero tolerance" attitude to racism in soccer.
Neither Eboue nor his club commented on the incident at the game but offensive chants by fans could be heard around the ground and media reports have suggested the abuse was racist.
Besiktas could be fined by the Turkish football federation for failing to control their supporters.
Duren added: "These are baseless allegations and should not be taken seriously, Besiktas fans have always had extra sympathy for African players because of the club's black-and-white colours.
"It's true that Turkish football has many issues to resolve, but racism is simply not one of them."