Gareth McAuley was sent off in a case of mistaken identity for West Brom after 90 seconds at the Etihad Stadium when Swarbrick failed to spot that Craig Dawson had been the culprit in bringing down Wilfried Bony when he was through on goal.
"These decisions change games," Pulis told BBC Sport. "In the modern world today refereeing is a tough job.
"I speak for a lot of managers in the professional game that the standard of refereeing hasn't been good enough this season.
"If we can help them with a 30-second call-back option, say two times in a game, it would stop us talking about the referees and more about the game itself instead.
"If we can help them in shape or form we should."
West Brom resisted for 27 minutes before Bony fired City in front with his first goal for the club and Brazilian midfielder Fernando made it 2-0 before halftime from a corner.
David Silva added a third after the break.
Pulis was unhappy with the build-up to the hosts' second goal though.
"The second goal shouldn't be allowed," Pulis told BT Sport. "Fernando kicked Saido (Berahino) in the face while jumping and it's a decision which leads to the second goal and kills the game.
"Let's be fair, it was going to be tough here today. Saido missed a great chance to make it 2-1 but obviously it's a game that was decided in the first couple of minutes."
Defeat for West Brom leaves them in mid-table with 33 points from 30 matches.
(Reporting By Michael Hann; editing by Martyn Herman)
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