"I can't talk for Middlesbrough, I can only talk for us as it's near desperation," Moyes told a news conference on Tuesday. "The only thing I have got in my head is how to beat Boro.
"There is a belief in the squad we can get three points tomorrow night. It is important we give the fans something to cheer about."
"We are really focusing on staying in the Premier League. If we win this next one, it gives us a real chance on Saturday."
Sunderland striker Duncan Watmore may need a second operation on his injured knee after suffering slight discomfort on his return to light training, Moyes said.
The 23-year-old was ruled out for the rest of the season after damaging his anterior cruciate ligament against Leicester in December.
"Obviously he's (Watmore) not back, but he might be needing a little bit more surgery on his knee," Moyes added.
"He's been feeling it. He's been running a little bit, so he'll see the surgeon this week."
Sunderland have won just twice on the road all season, while Middlesbrough are winless in their last 16 league games.
(Reporting by Hardik Vyas in Bengaluru; Editing by Hugh Lawson)
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