Acerbi was provisionally suspended last week by an Italian anti-doping agency after he failed a test for high levels of the human chorionic gonadotropin (HCG) following his team's Serie A victory against Cagliari on December 1.
The 25-year-old Acerbi, who underwent an operation for testicular cancer in July, told Italian TV Italia Uno: "I have never taken any illegal substance and it's painful to be accused of that.
"I understand that the press has a job to do but these accusations have been very annoying, not so much for me but for my loved ones."
Sassuolo confirmed Acerbi was not undergoing any treatment and, therefore, had not requested any special dispensation for the former AC Milan and Chievo player.
High levels of HCG can be produced by a cancerous tumour.
"The high level hormone can be a consequence of many things," Acerbi said. "I will have some tests done.
"My main concern right now is my health.
"You cannot point the finger at someone without knowing the situation. I demand respect for my health and for my family.
"I've had doping tests done before the game against Cagliari and had I taken something, I would have already tested positive before that.
"Those that have branded me as a cheat have disgraced me, my club and my doctors."