Saints' 2-0 loss at Aberdeen on Saturday left them without a Clydesdale Bank Premier League win in four matches ahead of the Boxing Day Tayside derby at Tannadice.
"If we're as good as we can be then I think we can beat anyone in the league," Mannus said.
"It's just whether we are or not. Hopefully we can recover and get ready for that.
"There's no reason we can't win. It's important come Wednesday we're ready to go. It's a big game for us."
After making numerous saves to keep Saints in Saturday's contest with Aberdeen, only for Niall McGinn to score twice in the final 30 minutes, Mannus hopes to have a quieter Boxing Day.
However, the Northern Irishman knows United have the quality to trouble his side, despite a tame goalless draw in the first meeting between the sides earlier this season.
He added: "Last time we played them we drew 0-0 at home. It was a bit of a boring game, I guess.
"Last time I didn't really have a lot to do; I don't think they had too many shots last time. Maybe it was just a one-off game.
"With (Jon) Daly and (Johnny) Russell and some other players, I guess you do expect to be quite busy. I'll be ready for it."