Before half-time, Cavani was adjudged to have elbowed Chiellini in the face while the Italy international was seen to pull the Uruguayan's hair.
Despite their on-field exchanges, Chiellini has assured that there are no hard feelings between the two.
“We spoke afterwards and it’s only right that for 90 minutes we knock each other about, but at the final whistle it’s all over," Chiellini told Sky Sport Italia.
“What happened can be seen on the footage. It stays on the pitch - it is a great challenge to be taking on champions.
“It was an important game that wouldn’t decide anything, but we sent a signal we want to win the Scudetto again and deserve to be top of the table,” continued Chiellini.
“It was a decent performance and we hoped to win, but the draw is overall the right result.”
Chiellini was a doubt to play before the match but managed to play the full 90 minutes and even got himself on the scoresheet.
But he admitted the match had taken its toll, explaining: “The ankle still hurts a lot.
"I have to thank the medical staff, as we worked together all day and even at night at my home.
“I am glad that I was able to help the team, though I still need to improve my fitness levels and I can only do that by playing.”