The incident occurred in the second minute of the clash at the Etihad Stadium, when Craig Dawson fouled Wilfried Bony, but McAuley was the man incorrectly given his marching orders by Neil Swarbrick.
Pulis was also unhappy with City's second goal, scored by Fernando, suggesting that Saido Berahino - who later hit the crossbar from point-blank range - had been fouled in the build-up.
"If they're saying they're the laws of the game then the lad has to be sent off – fine," Pulis told BT Sport. "But how he gets the lad wrong is just absolutely amazing.
"The second goal shouldn't be allowed, Saido gets kicked in the face. It's a decision that leads to the second goal and kills the game.
"It was going to be tough here 11 against 11. Saido's missed a great chance to make it 2-1. It was a game that was decided in the first couple of minutes."
Pulis recommended a new system be implemented to avoid such decisions being repeated.
"We obviously don't have a say what the refs do or what they don't do, but it affects us," he said.
"But if you're given that opportunity where the referee can have a 30-second call-back - I'd have two 30-second call-backs for each manager in each game. That eradicates all the stuff that we're going to be talking about now."
The result leaves West Brom still looking over their shoulders at the bottom three, with key matches at home to QPR and Leicester City up next.
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