The Yorkshireman pleaded guilty and has been suspended for the remainder of the NRL regular season following the dangerous contact on Wests Tigers hooker Robbie Farah.
Dewsbury-born Burgess was banned for four games after a previous eye gouge on New Zealand's Dallin Watene-Zelezniak when the Kiwis toured England last November.
The NRL reported that he conceded to the judiciary that “my career is probably in the balance” and “what I've done looks pretty disgraceful on the footage there.”
But Burgess - who started out in Bradford Bulls’ academy before beginning his career with Souths - insisted it was not a deliberate act and “I swear on my kids lives I didn't know I had my hands in his eyes.”
Burgess, 27, is out of contract at the end of the season and is hoping to get a new deal at Souths where he debuted in 2012 but he may struggle to get a contract there or anywhere else in the NRL.
Super League clubs will be monitoring the situation and Burgess maintained: “I'm definitely going to change the way I play.
“I'm going to be a lot more cautious ... I will be more careful."