The Capital One Cup semi-finalists will head into Christmas with just 10 points banked from their opening 17 Barclays Premier League games, and they will need a turn-around of epic proportions if they are to match West Brom's feat of escaping the drop after entering the festive period at the foot of the table.
Poyet's men were unable to reprise their midweek heroics against Chelsea as they struggled to create clear-cut chances in a goalless clash, and their fortunes took a further turn for the worse when defender Wes Brown was sent off in stoppage time.
Poyet said: "We are losing time, we are losing games. I said in the beginning after winning a couple, we needed to win 11 to think, 'Can we get to 40 [points]?', and we can't win a football game, so who are you going to blame?
"This is where we are. The quality is what you see, there is no more.
"I was not expecting this. I have always said I hate excuses - until now for some reason, we have always had an excuse and people can use it.
"Today, we have not. Today was a day to win and we didn't, so we are responsible for where we are and it's getting more and more difficult.
"It would be very nice if somebody could tell me why we are at the bottom, and if you think it's because of me, I'll take it if it's not personal.
"I have always accepted criticism from the press. If it's fair, I take it. If it's me, it's me. That's where we are."
Norwich created the better chances in a poor first half with Nathan Redmond and Gary Hooper calling keeper Vito Mannone into action, and the Black Cats offering little of note until Phil Bardsley tested John Ruddy with a long-range 37th-minute effort.
However, Sunderland rallied after the break with Brown heading against the outside of an upright, although substitute Ricky van Wolfswinkel should have put the visitors ahead eight minutes from time, only to be denied by Mannone.
Opposite number Ruddy almost handed the Black Cats victory seconds later when he raced from his line in a vain attempt to beat Fabio Borini to the ball, but when the Italian squared for Ki Sung-yueng, the South Korea international fired over the unguarded goal.
Poyet said: "I expect somebody to score. It doesn't have to be Ki all the time, but it has to be somebody.
"The decisions in the last 30 metres today were scary, and that was unexpected - players who needed to have a shot, taking three touches, players who need to take a touch, they try to shoot, back to goal.
"I didn't expect that. I have got no explanation. Now if we make a mistake, I can tell you why, but there were things today that happened on the pitch that are difficult to explain."
The Uruguayan declined to comment on Brown's sending-off after he clattered into Van Wolfswinkel close to the sideline, but Norwich boss Chris Hughton thought referee Martin Atkinson had got it right.
He said: "The challenge was certainly reckless, there's no doubt about that.
"It's a shame because it was a whole-hearted game, both teams ended up having a real go. At one stage, it was pretty end-to-end and it was a shame, really, because it wasn't that type of game.
"They have had a good week, Sunderland, and that can really buoy a team.
"Irrespective of any difficulties they have had, they have still got very good players, so in this day and age any draw, particularly with a clean sheet, away from home, that's a good draw."