While Tate stopped short of saying the decision to award Sharks winger Beau Ryan a try on the seventh tackle had cost the Cowboys the game, he admitted it did have a "huge bearing" on Saturday night's 20-18 defeat at Allianz Stadium.
"When you walk off the field and hear what's happened it makes it pretty hard to swallow I can tell you," an emotional Tate told AAP.
"It's obviously a mistake, but far out. That's the basics of the game: keeping the tackle count.
"I just don't understand how it could happen.
"The thing that's disappointing is that we're all meant to cop it sweet and just walk on and go on.
"...Something has to be done."
The controversial play happened at the very ground that a video referee howler cost the Cowboys a semi-finals berth in a match against Manly last year.
Labelling the 2012 decision over a Kieran Foran knock-on as almost short of a joke, Tate was at a loss to describe the latest mistake.
"It's two years in a row that we've been (dudded). We haven't had any favours coming down here," Tate said before echoing his coach Neil Henry's suggestion of a conspiracy.
"I don't know, maybe they want a couple of Sydney teams in the grand final? You tell me. I'm not sure.
"Everyone's got hopes and dreams of going on and playing finals and making grand finals, but it's not meant to be (for the Cowboys)."
Regardless, the Queensland and Australian Test centre said the controversy did not detract from the Cowboys' success in posting six back-to-back wins after Henry was told his services were not needed in 2014.
"It doesn't because it's been a huge effort for us to get here," he said.
"And it's because of Neil's class and the character that he's had and the respect that he's got from everyone that we've got in here.
"But let me tell you, it doesn't sit well with me mate."