Brown, who was travelling at considerable speed, won the ball with the challenge against Charlie Adam and replays suggested any contact between the two players had been minimal.
Kevin Friend's call drew an angry reaction from Poyet and, when asked about the incident after the match, the Uruguayan manager said: "I would like the referees' association (the Professional Game Match Officials Board) to apologise to me this time.
"They did it last week. I think it is fair - they called a British manager and I think it is time for them to call a foreign manager.
"Then, the referee will have said it was not a red card and I don't need to appeal."
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