On the back of an impressive Capital One Cup victory over Chelsea in midweek, and an improved performance at West Ham last weekend, a home tie with Norwich seemed to be the perfect opportunity to grab a much-needed Premier League win.
However, the Canaries had other ideas, and stifled any threat that the Black Cats threw at them all afternoon.
"With all respect to Norwich, we do not have any excuses here," he told Sky Sports.
"They are not in the top seven. I don't like excuses."
Poyet did not discuss Wes Brown's late dismissal, but seemed to be downbeat after the draw.
"I feel very disappointed as it was time to win a football game," he added.
"Everything was set on the day, the way we have been improving, the way we came out of the game with Chelsea in midweek, the opposition, the timing, but again no.
"Confidence was high in the dressing room. This makes it more disappointing."