The pair clashed twice during the contest, with Van Persie instigating the sending off of Dusko Tosic, before overtly celebrating his winner.
Van Persie, 33, raced towards Ozyakup after scoring, before sliding on his knees in celebration beneath the nose of his former Arsenal team-mate.
"I was very good friends with a certain player on the field. That changed today. Sometimes you see the real face of a footballer on the field," Ozyakup said, after the incident.
Van Persie was originally given a three-game ban by the Turkish Football Federation, but it was reduced to two matches on appeal.