"The ruck was all over the shop. It was very frustrating.
"We can't use that as an excuse. At the end of the day, we weren't good enough. We didn't win, but I tell you what, we're struggling and so are they (the referees)."
Deputising for injured captain Paul Gallen, Graham was most frustrated by Thurston being awarded his second try of the night after he stripped Cronulla fullback Michael Gordon in an apparent two-man tackle.
"We see that decision tonight and we'll probably see it maybe in another another game over the weekend when the same thing will come up and it will be a different decision," he said.
"There's no use harping on it because, at the end of the day, what's happened has happened.
"But we review ourselves every week and for it to be round 20 and (the referees are) still struggling ... it happens in every game. Every game, you hear a captain talking about it.
"It's just frustrating and the game deserves better than talking about this.
"We should be talking about JT playing well, or something else about the game."
Cowboys fans will be talking about their team climbing back into the eight and about Thurston's latest masterful display.
After swapping his No 7 jumper for No 16, in honour of injured Newcastle star Alex McKinnon in the opening game of Rise For Alex Round, Thurston's signed jersey will no doubt fetch top price after he put the Sharks to the sword with two tries, six goals and endless torment.
Winless in Sydney since their last visit to Cronulla in round 25 last season - and anywhere outside of Townsville all year - the Cowboys were up 16-0 after just 22 minutes.
Aided by a glut of penalties, Cronulla briefly threatened another fightback win after going to halftime only trailing by four points thanks to quickfire tries to Jonathan Wright and Luke Lewis.
But it was one-way traffic after the break.
"It's good to get the monkey off the back," said Cowboys coach Paul Green. "Really pleased with the result."
The only concerns for the Cowboys were forward Ashton Sims and five-eighth Robert Lui being placed on report for first-half high tackles on Sharks pair Jacob Gagan and Andrew Fifita.
- AAP