The Black Cats head for Norwich on Saturday for the latest in a series of Barclays Premier League six-pointers with both clubs firmly entrenched in the battle to drag themselves clear of the drop zone.
Poyet's men passed up a golden opportunity last weekend when they drew 0-0 with fellow strugglers Crystal Palace at the Stadium of Light to extend their recent run to just one win from eight league games on their own pitch.
With their final five fixtures on the road taking them to Liverpool, Tottenham, Manchester City, Chelsea and Manchester United, Sunderland know three points at Carrow Road could prove invaluable in what is likely to be a hugely tense conclusion to the season.
Poyet said: "Everybody is going to try the same, and the team that panics least is the one which is going to stay up.
"The ones who are not too nervous or they forget about playing and don't do what they are capable of doing, they are going to lose too many games.
"Yes, we need to be brave, brave as a team. Of course, the more brave players on the pitch, the better team you have got.
"We are in a situation where we need to believe it is possible and maintain at least the level of performances and the quantity of points we have got so far during the time I have been at the club.
"If we maintain that, we are going to be all right."
Poyet is convinced that his methods, which have yielded 24 points from the 20 league games for which he has been in charge to date, will take the club to where it needs to be.
The Black Cats had only a single point from seven games when he arrived on Wearside in October last year, but his confidence that they would stay up has never wavered.
He said: "I ask the players to maintain the level of performance and the level of results we have had during my time here, and if we maintain that and we add another 12 or 13 points and we don't stay up, that's what we were about.
"People said when I got here, we needed a miracle and it was going to be impossible.
"I don't want to have any regrets. If we have 30, 31 games in charge and we get nearly 40 points and we don't stay up, I don't think it's my fault."
Sunderland might have gone into the weekend sitting in 17th, rather than 18th, place had they made the most of their opportunities to beat Palace.
They could also have lost that game at the death when Kagisho Dikgacoi was presented with a gilt-edged chance, but in Poyet's eyes, that would have represented the kind of daylight robbery from which his side have themselves not benefitted all season.
He said: "That game when you really play terribly, 90 minutes of terrible football, awful and the opposition deserves to win 3-0 or 4-0 and then you go and you nick it somehow, we haven't had that.
"We have had it the other way. We deserved to win easily at Aston Villa and West Ham and we didn't, so I am waiting.
"People say it will come, in 38 games you will get something against and something for.
"If we keep performing, as I have always said in my time here, maybe one of those games will make you stay up."
Poyet will be without striker Steven Fletcher, who is waiting to discover the extent of his ankle injury, but otherwise has no fresh fitness concerns.