United are currently in 12th position in the league table after three defeats in the first six matches of the season, but Moyes is confident that his side can turns things around.
The 50-year-old told reporters: "Manchester United is a good club, I am sure that they know that they picked the right man for the job. Sir Alex was part of that process as well.
"It's a long season. We'll hang in there and get ourselves as close to the top as soon as we can."
The former Everton manager takes his team to the Stadium of Light to play Sunderland on Saturday evening.