Poyet's side, already 1-0 down at the time, were reduced to 10 men in the 36th minute of the Barclays Premier League contest when referee Kevin Friend deemed a sliding tackle from Wes Brown on Charlie Adam to be worthy of a straight red card.
Brown, who was travelling at considerable speed, won the ball with the challenge and replays suggested any contact between the two players had been minimal.
In the five league matches Poyet has overseen since he succeeded the sacked Paolo Di Canio at Sunderland - who are now back to the bottom of the table - there have been three Black Cats players sent off.
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.
Gus Poyet: "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.
"I'm not going to comment on the referee because I don't want to get fined.
"Did you see the action? Look at the computer - if you want, we will watch it. If you didn't see it, feel free to do so, from every angle.
"Charlie said he (Brown) touched his shinpad but he kept running - he didn't go down (immediately) and he is not in hospital.
"There is no doubt about it. It was the referee who made the decision and he took three or four seconds to give the foul, which was not even a foul."
"Are we getting a reputation with referees?
"It's a good question and I think we should ask Mike Riley.
"He could tell us that. Let's see what they tell the referees inside. Let's see what they do next week when we make a tackle."
PREMIER LEAGUE FIXTURES ...
Sunday November 24
13:30 Manchester City v Tottenham
16:00 Cardiff City v Man Utd
Monday November 25
20:00 West Brom v Aston Villa
Sunderland Fixtures
Saturday November 30
15:00 Premier League Aston Villa v Sunderland
Wednesday December 4
19:45 Premier League Sunderland v Chelsea
Saturday December 7
17:30 Premier League Sunderland v Tottenham
Saturday December 14
15:00 Premier League West Ham United v Sunderland
Tuesday December 17
19:45 League Cup - Qtr Sunderland v Chelsea
Saturday December 21
15:00 Premier League Sunderland v Norwich City
Thursday December 26
15:00 Premier League Everton v Sunderland
Saturday December 28
17:30 Premier League Cardiff City v Sunderland