The Black Cats were trailing 1-0 at the Stadium of Light when Emanuele Giaccherini stabbed home from close range, only for an offside flag to halt his celebrations.
Replays suggested the Italy international had been harshly treated, but a dismayed Poyet was in no mood to blame the assistant referee for a hugely disappointing result.
He said: "It could be a good excuse, that the referee [Mike Jones] was poor. 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 5ft 6in player behind a 6ft 2in defender. Incredible.
"He probably saw the top of his hand and gave him offside. That is the excuse of the day.
"The linesman did something we were not expecting. Sometimes these things go for you, here it went against us. If you want an excuse, you get one."