Touch judge Bryce Lawrence brought the incident to the attention of referee Christophe Berdos and was heard to recommend a minimum of a yellow card.
Some of the Lions players believed Berdos should have given Burger a red card, leaving the Springboks with only 14 men for 79 minutes.
"I was surprised that someone of Burger's quality would have done something like that. I felt the fingers around my eyes," said Fitzgerald, who was making his Lions Test debut on the left wing.
"It seems to becoming a part of the game that we would rather not be there. You would hope that if a referee finds something like that he will deal with it severely.
"I went into the ruck, got cleaned out and felt a hand going for my eyes.
"Given the seriousness of the allegations you would have to say it was probably a red card offence."
Scrum half Mike Phillips was also incensed by the eye gouging and many other off the ball incidents during a hugely physical
"It was a clear red card -. tt was simple," said the Welsh international.
"They should have played with 14 men for 79 minutes, and that would have given us a massive advantage.
"I couldn't believe it. You can't do things like that and it was a disgusting game really.
"There were a number of punches thrown off the ball and other things that went on that were illegal.
"I understand that Test rugby is a tough environment, but you have to stay within the rules.
"I heard a quote from Peter de Villiers that it might be part of the game, but to me that is never part of the game. I am very disappointed he said that.
"I can't see that ever being part of the game. It certainly wouldn't be part of a game I want to be associated with."
Both Burger and South Africa lock Bakkies Botha were suspended following disciplinary hearings by Judicial Officer Alan Hudson of Canada that concluded in Johannesburg on Monday.
The pair was cited by match citing commissioner Steve Hinds of New Zealand for foul play during Saturday's second Test.
Burger was found guilty of committing an act contrary to good sportsmanship - Law 10.4 (l) - by making contact with the face in the eye area of Lions winger Luke Fitzgerald in the first minute of the Test.
He was suspended for eight weeks and will only be able to return after August 22, ruling him out of three of the Springboks' Tri Nations fixtures.
Meanwhile, Botha was found guilty of transgressing Law 10.4 (j) by dangerously charging into a ruck without binding on a player.
The incident took place in the fourth minute of the second half and resulted in Lions prop Adam Jones leaving the field with a shoulder injury.
He was suspended for two weeks, effective until midnight on July 11.