Poyet's side have drawn four and lost one of their previous five games and have not tasted victory at the Stadium of Light since October 4.
West Ham, by contrast, have won three on the bounce and have only lost once in their last nine as Sam Allardyce's men continue to surprise many by occupying a spot inside the top four.
Sunderland's last three matches saw them pick up goalless draws against Chelsea and Liverpool, either side of a 4-1 thumping by Manchester City.
"We knew the challenge of last week and we knew it wouldn't be easy to play against Chelsea, Manchester City and Liverpool, so after competing with them and picking up a couple of points the idea is to now go one step ahead and start winning football matches," Poyet told the club's official website.
"I don't think it's going to be easier, it is just a different challenge and a different way of playing, so we need to make sure we can cope with the way West Ham are playing at the moment because they are doing very well.
"We need to think about what we do well and what we do best to win the game and get three points, because we're in a situation where putting a couple of wins into the table would make the rest of the season easier."
Sunderland, in 14th, currently lead a pack of seven teams separated by five points at the bottom of the table, a far cry from the heady heights reached by Saturday's opponents.
Despite West Ham's lofty position and strong form, Allardyce is anticipating a stern challenge when they travel to the north east at the weekend.
"They're hugely difficult at home, playing them away has been tough for us," he said in a press conference on Thursday.
"They've been struggling for goals recently. I think Connor Wickham and Steven Fletcher would've wanted a few more goals than they've got and if they had they would have converted their draws to wins.
"Hopefully we can keep those guys quiet on Saturday and deliver another good away performance."
Allardyce revealed on Thursday that Mark Noble remains out with an Achilles problem, while full-back Carl Jenkinson is a doubt after coming off in the 3-1 win over Swansea City last time out with a hamstring injury.
For the hosts, Patrick van Aanholt (shoulder) is still out, Emanuele Giaccherini (ankle) and Billy Jones (hamstring) will return to training next week, and Steven Fletcher comes back into contention after sitting out the draw at Liverpool with a knock.
