The Portugal international, who joined Fener from Chelsea in the summer, was sent-off after collecting a second yellow card in the 2-1 defeat.
Referee Halis Ozkahya accused Meireles of not only spitting at him as he challenged the decision but also directing a homosexual gesture in his direction, claims denied by the player.
Meireles said: "I'm really annoyed at being accused of spitting at the referee. I have an eight-year-old child, can you imagine if kids at school start saying your father spat at a referee? This could ruin my reputation in the eyes of my child.
"I have many gay friends who I deeply respect. The hand gesture I made is directed at the referee caving in to the pressure of the home fans.
"That hand gesture was to tell him he was scared. Look at my hairstyle, what I wear, I'm not a prejudicial person, my hand gesture was in no way, shape or form a homophobic one.
"I don't know what the hand gesture for calling somebody gay is in Turkey but what I did was entirely based around the referee being a coward and bowing to the pressure.
"The referee's accusations are outrageous and defamatory. I will be taking legal action against him to prove my innocence."
The Turkish Football Federation have stood by Ozkahya's version of events, however.
Fener issued a statement indicating they would appeal, calling the punishment "unfair, unfounded and not acceptable".