The sides meet for the second time in less than a fortnight at the Stadium of Light on Tuesday evening with a semi-final berth at stake as they take a break from very different league challenges.
Chelsea will arrive on Wearside, where they claimed three points on December 4 with a narrow 4-3 victory, sitting in third place in the table and only two points behind leaders Arsenal.
By contrast, the Black Cats are marooned at the bottom, five points shy of safety and in danger of being cast adrift unless they can revive their fortunes sooner rather than later.
Poyet said: "If we want to get out of the relegation zone, we need to become winners, winning football games, and to become winners, we need to win the next one, so let's see if we can use it for that reason.
"It's important. It's a cup competition. We are losing a little bit of belief in England in the cups because of course, the Premier League or the Champions League means everything.
"It's a competition and you cannot start the season thinking, 'I won't care about this one, I will care a little bit about this one and only care properly about this one'.
"It's just about playing and becoming winners. A winner is somebody who wins most of the time, and that's what we are trying to achieve here."
On paper at least, few would give Sunderland much chance of booking a place in the last four no matter which 11 players Blues boss Jose Mourinho sends out.
However, Chelsea had to come from behind and withstand a late onslaught on their last visit, although Poyet acknowledges that will count for little this time around as he attempts to deny his former club a chance to add another trophy to their honours list.
He said: "To get there, we need to beat a very top team, so we need to be very good tomorrow. We need to be much better than two weeks ago."
The 46-year-old Uruguayan could be forgiven for treating the cup as a secondary consideration with Saturday's home clash with Norwich likely to play a more central role in the destiny of the club's season.
However, he is adamant that the showdown with the Canaries will not even enter his head until the final whistle sounds on Tuesday night.
Poyet said: "I am trying - it's not easy because of the situation we are in - but I am really trying to concentrate only on tomorrow, so I am not watching Norwich, I am not reading any news about Norwich.
"It's all about Chelsea now. Now, I am sure as soon as the game is finished, it's going to come into my head, Norwich, Norwich, Norwich.
"But for now, I don't want even to think about it."
Poyet, who will once again be without midfielder Jack Colback because of a virus, returned to work on Monday morning after Saturday's 0-0 draw at West Ham knowing he faces a crucial few weeks if he is to drag the Black Cats out of a hole.
He did so with two of his Premier League counterparts, Steve Clarke and Andre Villas-Boas, having been relieved of their duties at West Brom and Tottenham respectively.
Asked if he felt safe in his job, Poyet replied: "I never think about it.
"I just try to do my job and if one day you get a phone call and you need to go to see the chairman, then you will think, 'Oh, here we go'. But at the moment, I am just thinking about doing the job."