The Hammers make the trip to the Theatre of Dreams following an impressive 3-1 win over Liverpool at Upton Park last weekend.
While the hosts are sure to be favourites to win the match, Poyet believes that West Ham can cause an upset against Louis van Gaal's side.
"We believe we can not only match them but beat them and get more points on the board from our trip to Old Trafford. That would be even better for the team," he told the club's official website.
"We're coming off a win and they're coming off a loss, so you never know. We'll give everything and hopefully we'll get something."
Poyet has made two appearances for West Ham this season after joining the club from Charlton Athletic over the summer.