The official was in charge of Stoke's heavy 5-1 Boxing Day defeat at St James' Park, a match that saw the visitors reduced to nine men before half-time with Glenn Whelan and Marc Wilson both receiving their marching orders.
Manager Mark Hughes was also sent to the stands for dissent, for which he was subsequently charged by the Football Association, while Newcastle's second goal was contentious as the ball appeared to be out of play before Hatem Ben Arfa crossed for Yoan Gouffran to head home.
Coates insists he is not looking for excuses for the loss, but is demanding an explanation for what he considers a series of errors from the officials.
He said: "The performance of the referee and his officials was a disgrace, and we will certainly be complaining to the relevant authorities.
"We cannot accept what happened to us at Newcastle without making some form of representation.
"It's then up to the officials what they do, but we found it hugely disappointing because there were so many poor decisions.
"There was no common sense applied and I don't think either of the yellow cards for Glenn Whelan were deserved.
"For one of the goals I could clearly see the ball was out of play, sitting high up in the stands.
"The sendings-off completely changed the game. We were playing ever so well up to the dismissals, leading one-nil, but when you're down to nine men you've got no chance.
"It's not a case of sour grapes, we simply cannot accept what happened."
