Smith has reluctantly taken the early guilty plea on a charge of contrary conduct, meaning the Australian hooker will be available for Sunday's NRL match against Cronulla at Olympic Park.
But Storm chief executive Brian Waldron lashed out at the Warriors for denying Tate permission to make a statement or appear on behalf of Smith at a judiciary hearing.
"We begrudgingly accepted the charge on the basis we were unable to get the opposition player (Tate) to make a statement or be available for the hearing," Waldron said.
"Despite the player's willingness to cooperate, the club refused to make him available.
"We will be addressing this issue with the NRL as we think it's a ridiculous situation.
"We will be seeking clarification from the NRL as to why, in the interest of fairness, they do not have the power to enforce the player to make himself available for questioning.
"This has clearly interfered with our ability to defend the charge. That cannot be in the best interests of the clubs or the NRL."
Smith said he believed his tackle was fair but contesting the charge posed too great a risk.
"I'm disappointed to have been charged considering there were many tackles similar to mine in every game over the weekend," said Smith.
"I find it hard to accept that I was singled out.
"If you look at the vision closely, it shows I haven't applied any pressure to the neck, my arm is wrapped around his chest.
"I have been a vocal supporter of outlawing any tackles that place unnecessary pressure on the head and neck and I applaud the NRL for trying to stamp it out, but that is not the case in this situation."
The early guilty plea means Smith will carry 93 points into any charge he receives in the next two years.