The Istanbul club emphasised their record when it comes to the fight against discrimination and promised to take "any necessary steps" if their player is found guilty
Television cameras appeared to show the former Newcastle United midfielder aim a racial slur in the Ivorian's direction during the fiery clash, a claim which Zokora backed up in the post-match press conference.
The incident is being investigated by the Turkish Football Federation, who could slap an eight-match ban on Emre if he is found guilty of the charges.
In a statement released on their website, Fenerbahce stressed that they did not approve of such a sensitive issue being brought to public attention, but pledged to take action of their own if needed.
"For our club, the fight against discrimination is crucial, and we have a solid and consistent record with regards to eradicating such issues," the statement read.
"Although we have considered the reaction of the players, we do not approve of such a sensitive issue being addressed at the end of the match.
"Fenerbahce sports club will take any necessary steps against a person suspected of making racist remarks, and will not tolerate it."
Emre has previous when it comes to accusations of racism after he was charged with using racially-aggravated language during his Newcastle days in an incident against Everton in 2007.