The former Everton manager has had a rocky start to his tenure and "is under a bit of pressure" but the England forward feels that it is the players who have been under performing.
Despite coming from behind to beat Sunderland on Saturday, the Red Devils are only ninth in the Premier League table after seven games.
Rooney has urged his teammates to use the comeback against the Black Cats as motivation in the future, and says the squad is still adapting to Moyes' style.
"Obviously the manager is under a bit of pressure," Rooney told reporters. "We know as a team it's us who have let him down. We have to pull together for the manager and show the sort of fight we have done here and we'll be fine.
"It will be because it's a new manager with different styles and we have to adapt to them. We need to do better for him than we have been."
Adnan Januzaj was the hero for United at the Stadium of Light. On his first start, the 18-year-old scored twice to turn the game around and the England international was thrilled to see the youngster excel.
"He's a great prospect," Rooney enthused. "He takes the ball, he runs at players and he's got great ability. It's great the manager has thrown him into the side, especially with what has happened in the last few games. There was big pressure on us but the manager has trusted him and he has repaid that. He's very confident - that's great to see.
"A lot of the young players who come through are a little bit timid and shy but he looks comfortable and he's confident in his own ability, which you need to be. It was a brave move to play him in the circumstances and we’re delighted it's paid off."
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