The champions have lost three of their opening six Premier League games under the Scot and currently lie 12th in the standings with a return of just seven points.
But Moyes, who succeeded Sir Alex Ferguson's 26-and-a-half year reign in June, has confidence in his abilities and those of the United squad as he looks to climb at the table.
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"They're really good players. They know the standards they've set over the years - together we'll work to get it right.
"It's a long season. We'll hang in there and get ourselves as close to the top as soon as we can."
United's next test is the trip to the Stadum of Light to face managerless Sunderland.
Kevin Ball is taking charge of the Black Cats on a temporary basis and Moyes has warned his squad not to underestimate the struggling side.
"It's an important game," he noted. "We want to try and win it so we'll pick a team which we think can get a result.
"Kevin is very experienced. They look like they played quite well in the last two games."
Wayne Rooney is expected to be fit to face Sunderland on Saturday but Moyes admits that he is unsure of the latest on the striker's shin injury, adding: "I've not seen Wayne this morning so I couldn't give you an update yet."