Poyet's attacking philosophy won plenty of plaudits in his previous job at Brighton but he has urged Black Cats fans to be patient as he sets about moulding a struggling team in his own image.
Poyet said: "When you pay for a ticket as a fan you want to see something special and you want to be proud of your team. There is no better feeling than going back to your friends and talking about one great move or shot or save.
"For that you need quality and an identity and I'm sure we are going to have great times here, but it's a process. The priority is to win. The sooner we start winning the easier it is for the players to relax and understand the way we want to play."
Swansea once again go into the game without centre-back Ashley Williams, who has featured just once in their last six games with an ankle problem and is forced to sit out again.
Everton boss Roberto Martinez says Leighton Baines' role in England earning a place at next summer's World Cup in Brazil underlines the fact that he is one of the best left-backs in the world.
Baines returns to club duty when the Toffees face Hull at Goodison Park on Saturday and Martinez said: "Leighton's performance (for England) is something we see week in, week out.
"It is great when you see a player take that into his international duty. There are not many left-backs in world football who can produce what Leighton produced and that is very pleasing."
Top scorer Robbie Brady is set to return to the Hull squad just two weeks after undergoing an operation on a troublesome hernia which was expected to keep him out for up to a month.
West Ham take on Manchester City at Upton Park with Hammers boss Sam Allardyce refusing to rule out the possibility of striker Ravel Morrison pushing into contention for a World Cup spot.
Morrison starred in England Under-21s' midweek demolition of Lithuania and Allardyce said: "I think if he continues to be a regular player with the first team I can't see any reason why he wouldn't get noticed and maybe be pushing that way."
Newcastle have defensive problems for their lunchtime clash with Liverpool at St James's Park, with Fabricio Coloccini out with a groin injury and Jonas Gutierrez having temporarily returned to Argentina for personal reasons.
Malky Mackay will be glad to get back to football after emerging unscathed from a five-hour board meeting this week, with his Cardiff side hoping to pull off a major upset with victory over Chelsea at Stamford Bridge.
Chris Hughton's Norwich head for the Emirates Stadium to face Arsenal while high-flying Southampton will heap more woe on Manchester United boss David Moyes if they pull off an upset at Old Trafford.
Stoke striker Jon Walters is set to line up against West Brom after returning from a groin injury.
Tottenham travel to Aston Villa in the Sunday game while Crystal Palace and Fulham face off in a potentially pivotal London derby on Monday night.