"It's a massive ask for us now, but we're not relegated yet and we have a chance," Moyes told reporters on Friday. "We'll push as hard as we can and sometimes one game can make a difference. Hopefully that game can be this weekend.
"We have to get a bit luckier, and try a bit harder - whatever it takes. I think the players are giving everything they've got, I really do."
Moyes admitted Sunderland were too reliant on striker Jermain Defoe, who has 14 league goals this season. The team's next highest goalscorer is Victor Anichebe, with three.
"We've relied on Jermain a lot and I hope he has another half dozen before the end of the season, but others have to score as well," Moyes said.
Midfielder Lee Cattermole and Anichebe could start against United after making substitute appearances in the club's 2-0 loss to Leicester City in midweek.
"Lee Cattermole trained today and looked fine. His leadership has been missing and having him back is a good thing," Moyes said.
"Victor's up and running. We need him up to a level where he can make a difference. We're in a position where we have to take risks. Can he play 90 minutes? Probably not. Can he play some minutes? Yes."
(Reporting by Aditi Prakash; Editing by Andrew Bolton)
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