Adam Johnson's 90th-minute strike - his third goal in as many trips to St James' Park - secured a 1-0 victory over Newcastle, who have now lost four times on the trot to their arch-rivals for the first time.
It was just the Black Cats' third Barclays Premier League win of the campaign and while Poyet was thrilled by it, he is adamant it must be the start of a concerted push up the table as he prepares for Hull's Boxing Day visit to the Stadium of Light.
He said: "We always talk about confidence - there is no more confidence you can get than beating your biggest rivals in the last minute
If somebody thinks differently, they have never played football, never played a derby.
"Now next week, there are no excuses
Confidence should be high, so we are able to create chances against Hull
We need to put the ball in the net
That's the good thing, no excuses
These are the games I really like."
Even if Johnson had not snatched the points at the death, Sunderland would have made the short trip back to Wearside with plenty of positives to take after enjoying the better of a game in which they had passed up a series of earlier chances.
But had it not been for the excellence of keeper Costel Pantilimon, they might have been trailing with the Romanian keeping out goal-bound efforts from Ayoze Perez and Moussa Sissoko.
However, Johnson, who Poyet later revealed was on the verge of being replaced with nine minutes remaining, popped up at the death to convert substitute Will Buckley's lay-off from close range to spark mass celebrations in the away dug-out and among the travelling fans.
The Uruguayan said: "If you ask me right now - it's difficult for me because of the feelings I have got - if it's better to win 3-0 or to win a game scoring in the last minute, I don't know which one to pick."
For opposite number Alan Pardew, the emotions were strikingly different as he surveyed a third successive defeat inside a nine-day period which has dispelled much of the optimism which had been fostered during an improved run of form.
Pardew said: "Today was a key game because the two fixtures we had, Arsenal and Spurs, were difficult
But this game now compounds that and we have to lick our wounds and prepare quickly for Manchester United.
"We have a tough run of games - we knew that - over this period, and this was always going to be a critical fixture, so losing it is very disappointing.
"We still find ourselves in a healthy place in the league, and the job now it to try to build on that."
Source : PA
Source: PA