"You need to show me because I didn't see anything. Did you see it today or did you see what happened in other years?" Lugano said. "The worst of all was Chiellini's attitude ... as sportsmen leaving the field, crying and appealing against a rival."
On the field immediately after the match, Suarez looked relieved to have pulled out the victory in the heat of this tropical coastal city. If Uruguay had lost, it would have been knocked out of the World Cup
After taking off his jersey, Suarez walked to a corner of the stadium, clapped and flashed his toothy smile as he waved to the thousands of Uruguay fans chanting and cheering his name.
FIFA, soccer's world governing body, can sanction players with bans of up to two years. FIFA had no immediate comment.
FIFA Vice President Jim Boyle said on British television that Suarez had let himself down again.
"There is no doubt Luis Suarez is a fantastic footballer but, once again, his actions have left him open to severe criticism," Boyle, who is also chairman of the FIFA referees' committee, said from his home in Northern Ireland. "FIFA must investigate the incident seriously."
Chiellini said Suarez should have been kicked out of the game.
"Not sending off Suarez (was) ridiculous," Chiellini said. "It was absolutely clear. There's even a mark."
Suarez's status for the World Cup had been in doubt after he had left knee surgery just a month before it started. He missed Uruguay's 3-1 opening loss to Costa Rica, but returned with a flourish to rescue Uruguay with both goals in a 2-1 win over England.
After the victory, he claimed vengeance against some of the British media he accused of treating him badly.
This was supposed to be the World Cup where Suarez repaired his reputation. He tried to rebrand himself as a family man after the birth of his two children, a son and daughter.
Suarez said he regretted his previous biting incidents, telling the Mirror newspaper in London recently that he worried what his children will think.
"That thought almost hurts me more than the actual deed. The fact, as well, that I will have to explain one day to my kids that it was me, their father," Suarez said. "That has kept me awake at night many times ... I want to be a father they can be proud of."