The 46-year-old's stark assessment of the club's prospects came in the wake of Saturday's 2-1 home defeat by Tottenham, which left the Black Cats sitting at the foot of the table, still five points adrift of safety, but with fellow strugglers Crystal Palace threatening to cast them adrift.
Poyet remains hopeful of dragging his side out of trouble, and his chances of doing so could depend on what he is able to do in the January transfer window.
But in the meantime, he has left his players in little doubt as to what he expects of them after the momentum he hoped they had gained from a spirited display in defeat by Chelsea in midweek dissipated alarmingly against Spurs.
Poyet said: "You can't do it every now and then. With all respect, we don't get paid to do your job today but not tomorrow, and maybe on Wednesday but not on Saturday.
"At the moment, we are not good enough. Sometimes being honest doesn't mean that you are negative. I am not, I am very positive. I am realistic and at the moment, that's what we are.
"We want to keep going, yes. The desire, the fighting, the spirit - the players are trying their best.
"At the moment, it's not enough, so we will see how we are going to change."
It might have been so different for Sunderland had they been able to reach half-time unscathed after Adam Johnson had made the most of goalkeeper Hugo Lloris' blunder as he came for Ondrej Celustka's 37th-minute cross.
But just as they had done against Jose Mourinho's men, the home side conceded within minutes, with Paulinho stabbing home from close range after Nacer Chadli had headed back across goal.
Worse was to follow five minutes after the restart when Mousa Dembele burst past Jack Colback on the left and saw his driven cross cannon off defender John O'Shea's heel and fly past wrong-footed goalkeeper Vito Mannone.
The Black Cats have now scored five own goals this season, and their run of fortune took a further turn for the worse 15 minutes from time when they were denied what looked like a clear penalty when Sebastian Larsson's corner struck substitute Sandro's arm.
However in the meantime, Jermaine Defoe had twice struck the post as Spurs passed up a series of opportunities to extend their lead, and Poyet was in no mood to blame ill fortune for a damaging defeat.
He said: "Luck is once or twice. Five own goals in seven games, eight games? No, I'm not taking that, I'm sorry.
"I think we were lucky at the end because it could have been 5-1. At the moment, I see too many players of the opposition playing against us probably their best games of the season.
"Do you think that that's a coincidence as well? You have to be very naive to think that.
"[Chelsea's Eden] Hazard had his best game of the season against us; today probably [Kyle] Walker had his best game of the season against us. I can go on and on and on.
"It has become too easy to play against Sunderland and you have to take it.
"My job - I'm a head coach, I coach, I convince players what is the best way to play football. I try to convince them constantly.
"In training I show them, I tell them, I repeat to them and we keep doing it and we keep doing it.
"It's going to be like a hammer in your head constantly. Now if we can get it before Saturday, we have a chance. If we don't, it's going to be worse and worse, it's as simple as that."