Just 24 hours after Cardiff sacked their widely-respected manager Malky Mackay, Poyet hopes to take advantage by heaping more pressure on them.
"People keep forgetting we are unbeaten in four games - we're playing well," Poyet told the Sunderland website (www.safc.com) on Friday.
"It's up to us to keep that belief going."
Sunderland have won twice and drawn twice in four outings in all competitions since they suffered consecutive home defeats by Chelsea and Tottenham earlier this month.
On Thursday, they maintained their more disciplined defensive approach with a 1-0 win at Everton, recording their third clean sheet in four games during which they have conceded only one goal.
"The whole squad has to pull together - two games in three days is tough," added Poyet, following their win at Goodison Park, courtesy of a first-half penalty by Ki Sung-Yueng.
"We have quality players to call upon like Jozy Altidore and Adam Johnson who were on the bench, but we face a difficult match.
"They are fighting for their lives, but we need to make sure we're ready and perform to the best of our ability. We need to make it difficult for them on Saturday."
Cardiff lost 3-0 at home to Southampton on Thursday and are only four points ahead of Sunderland in 16th place in the Premier League.
(Reporting by Tim Collings; editing by Justin Palmer)
