United boss David Moyes has lost three of his first seven Premier League games in charge of the club, falling short against Liverpool, Manchester City and West Bromwich Albion.
Rooney believes that the players have let Moyes down during his first few months in charge, but believes that the fight shown to beat Sunderland 2-1 yesterday can be used as a building block for improved form.
He told The Mirror: "Obviously the manager is under a bit of pressure. 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 [a time of transition] 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."
United's comeback at Sunderland lifted them to ninth in the Premier League with 10 points from seven matches.