The Royals were on the receiving end of a debatable handball decision in their 1-1 draw against Cardiff on 19 March.
"Managers should have two calls per game," he said. "One in the first half and another one in the second."
"You can't see any instant replays, but you can have an instant call to the officials if it's a big decision."
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McDermott revealed he had been told - once replays had been studied - a handball was missed in the build-up to Cardiff's equaliser.
"I looked at the Leicester v Southampton decision on Sunday, and for me, it's a handball," he said.
"But, that's what football's about and people make mistakes. It's a hell of a difficult call to make in real time if you're a referee or assistant.
"People don't get these things wrong deliberately."
Cricket, American football and tennis are among sports which permit appeals against decisions by officials.
Reading boss Brian McDermott believes managers and coaches should be given two chances per game to appeal against contentious refereeing decisions.