The French defender eventually saw a second yellow card for another incident in the 74th minute as the Rossoneri lost 3-2 in Turin on Sunday.
"It wasn't a punch, it was a tussle in the box and he hit him on the back," the 46-year-old told Sky Sport Italia.
"If you want to call it a punch, then call it that, but there are a thousand different fouls like that in the box. He didn't even catch his face. It was absolutely not a punch."
Chiellini went on to score a minute after Mexes was sent off.