The midfielder left Napoli in the summer for a move to Inter and an open letter was published on the Partenopei website.
Gargano said: "I want to tell the people that the farewell letter they published was not written by me. It did not come from me. It was written by the club.
"I did not leave Napoli just because I was afraid of no longer being considered a first choice player.
"I am tired of hearing people talk without knowing how things really went. I do want to thank those who still today show me their admiration without any type of rancour."