Emanuele Giaccherini scored from Steven Fletcher's knockdown not long after the restart but the Italian was flagged for offside meaning Villa maintained their one-goal lead following Gabriel Agbonlahor's early opener.
Poyet believed the decision was wrong but could only use it as an excuse after a mediocre showing from the bottom-placed Black Cats.
"It could be a good excuse, that the referee [Mike Jones] was poor," said the Uruguayan.
"He didn't let us play when we needed to, he stopped the game a hundred times, he talked to everybody - the only thing missing was him making a phone call.
"And then the linesman - normally it should be very difficult for a person 50 yards away to see a 5'6" player behind a 6'2" defender. Incredible.
"He probably saw the top of his hand and gave him offside. That is the excuse of the day today.
"The linesman did something we were not expecting. Sometimes these things go for you, today it went against us. If you want an excuse, you get one."
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