The Black Cats head into Wednesday night's Barclays Premier League showdown with high-flying Chelsea at the Stadium of Light still five points adrift of safety despite an improved run of form, and knowing they need to make a move fast if they are to avoid another desperate scrap for survival.
Tottenham are due on Wearside on Saturday evening to complete a tough double-header, although Newcastle and Manchester City have both left empty-handed in their two most recent league outings on their own turf.
However, with the games coming thick and fast as the holiday programme approaches, Poyet is refusing to place further demands on his players.
Asked if he has set a points target to take the club into the new year, he said: "No, no. In terms of points, no.
"Mentally for me it is just better to think about the next game. But, of course, we need to win a few games before Christmas.
"Look, it's true that you look at the table. People who say they don't look at the table, they are probably lying.
"But for us, the aim is to keep getting points. We need to make sure that we win 10 or 11 games, that's the aim - it doesn't matter against who - and then we will see.
"If the rest are better than us, then you need to take it, but we can't do more than just look after ourselves and win football games."
Sunderland took their meagre points tally to eight at the weekend with a 0-0 draw at Aston Villa, although they headed back to the north-east convinced they should have been doing so with all three after one of their better performances on the road to date this season.
They were unable to take advantage of a series of chances at Villa Park, with Italy international Emanuele Giaccherini guilty of a glaring miss, and Poyet is conscious that a continued inability to find the back of the net - they have scored only three times in their last five league outings - could prove fatal.
However, addressing that issue against a defence marshalled by his former Chelsea team-mate John Terry could prove tricky.
Terry emerged from the ranks during Poyet's four-year spell at Stamford Bridge, and his subsequent success has come as no surprise to the now 46-year-old.
He said: "We knew he was a character because as soon as he came up and started training with us, even if he was very, very young, he was impressive and strong and committed and you knew he would be in the team sooner or later.
"He started playing with us and then, when most of the older ones started leaving, you knew he would be an option as a captain, so I am not surprised that he was picked.
"Now, to stay at a football club as a character for so long and have so many titles, you need to be a very special player."