Williams told NITV News on Monday there were "clowns in the audience that were yelling out racial jibes and abuse towards Dane".
Thurston - set to play his 250th game on Friday night for the Cowboys - said he was fortunate enough not to have been racially abused during his glittering career.
But the four-time Dally M Medallist was appalled at the prospect his Queensland State of Origin teammate Gagai had been the subject of racism.
"It would be very disappointing if that is true," Thurston said.
"I am hoping it is not. I haven't copped it. I have been very lucky in that regard.
"But there is no place for it. There could have been kids around whoever it was (yelling alleged taunts).
"They don't need to be hearing that sort of abuse."
Thurston said it hurt to hear the allegations from Newcastle, especially during what had been the NRL's Indigenous Round.
He said the league had done its best to eradicate that sort of behaviour via community programs run by various clubs and highlighted by the All Stars v Indigenous pre-season game held annually since 2010.
"I know the NRL are doing their part to close the gap," Thurston said.
"We have a number of indigenous programs run by clubs and we are seeing great results from that."
- AAP