The defender says the Liverpool attacker should have been sent off for allegedly biting him on the shoulder but the forward claims the incident has been blow out of all proportion
Diego Godin scored the only goal of the game with just nine minutes remaining in Natal, as the Celeste dramatically progressed to the last 16 at the expense of the Azzurri, who only needed a draw to go through.
However, Uruguay's success has already been overshadowed by Chiellini's claim that Suarez should have been sent off for allegedly biting him on the back of the shoulder when the pair clashed in the box shortly before the deadlock was broken.
The Liverpool striker, though, says that the incident has been blown out of all proportion.
"These things happen inside the penalty area," Suarez told Uruguay's Channel 10 radio station. "We were chest against shoulder. I also immediately suffered a blow to the eye."
Suarez preferred to instead hail his side for the way in which they recovered from surprisingly losing their tournament opener against Costa Rica by defeating both England and Italy to seal a place in the knockout stage.
"We were very strong," the attacker enthused. "We did a great job. I think that having started the World Cup badly and turning the situation on its head, we deserved to go through to the next round.
"I had no more energy [at the end of the game against Italy] - the heat was really strong - but I was calm.
"Then the goal [from Godin] arrived and we are very happy. Now we will celebrate and think of our next opponent."
Having finished second to surprise package Costa Rica, Uruguay will face one of Greece, Cote d'Ivoire or Japan in the last 16.