The Black Cats failed to build on their midweek win over Chelsea, drawing with Norwich at the Stadium of Light and saw defender Wes Brown red-carded
Poyet's men were held to a 0-0 draw by visiting Norwich City on Saturday and finished with 10 men following Wes Brown's late dismissal for a strong challenge on Ricky van Wolfswinkel.
After 17 matches, Sunderland remain rooted to the foot of the table, four points from safety.
"I'm realistic. Time is running out," conceded Poyet.
"We're losing time and losing games. We were very poor technically today."
Poyet refused to comment on the red card given to Brown, who was also sent off at Stoke last month only for the decision to be rescinded.
"I'm not going to comment on any decision by the referee because it's not worth it," added the Uruguayan.
"When you're down the bottom you lose a player you don't want to lose, or the decision doesn't go your way. There's always something - that's life at the bottom."
Poyet was at a loss to explain why a side who had beaten Chelsea in the League Cup quarter-final on Wednesday could put in such an insipid performance.
"I was not expecting this," he said.
"I always say that I hate excuses and until now for some reason we always had an excuse but today, no.
"I don't look for excuses. This is reality. If someone wants to hide it's going to be difficult because in football there is no place to hide."
Poyet elaborated on his side's deficiencies, criticising the decision-making of his team.
"The decisions we made in the last 30 metres were scary," he said.
"Players who needed to have a shot were taking three touches and players who needed a touch were trying to take a shot. There were things that happened on the pitch that were difficult to explain."
Sunderland travel to Everton on Boxing Day before visiting Cardiff two days later and Poyet knows there is a lot of hard work to do before then.
"I need to make sure that we recover well and are in shape and analyse Everton," he said. "We need to go with a plan and we've got to be better. We'll see on Boxing Day.
"It would be nice if someone can tell me why we are at the bottom.
"If someone says it's because of me I will take that, if it's not personal I always accept criticism from the press. If it's fair, I take it; if it's me, it's me."