The 24-year-old was benched for the trip to Roma.
"Gasperini was clear after the match with Roma, with his choice geared towards allowing the boy to catch his breath after so many matches played close together," Ilicic's representative Amir Ruznic told Calciomercato.it.
"Josip has had no problems, he calmly accepted the decision of his Coach, as evidenced by the way he entered the field [as a substitute] and his determination shown on the pitch.
"Did the Coach jab the boy? Absolutely not and I think many have misunderstood the meaning of his words. Gasperini yesterday said that Ilicic does not have the quality to play for Paris Saint-Germain, but he wanted to reduce the weight of expectation and pressure against him.
"A part of the Press has often blamed Josip for the poor mistakes of Palermo, believing that only he can solve the team's issues. Since Gasperini's arrival his performances have grown significantly and his words are a clear certification of defence.
"Will Ilicic leave in January? Last summer at least seven clubs expressed an interest in the boy, but at this time he is fully focused on doing well with the shirt of Palermo."