Moyes lost three of his first six Premier League games in charge at Old Trafford, but United have since bounced back with four wins from their last five domestic matches.
Rooney believes that United needed time to become familiar with the way Moyes works but have now turned the corner, relishing the chance to climb the table and make up lost ground.
He told The Mirror: "We had a whole new set-up and different ideas from the manager.
"It's up to us to try and implement those ideas as best we can. It was a bit of a change but we're starting to show the things that the manager wants. Eight matches unbeaten is a good run.
"We're confident at the minute, we're getting more clean sheets and we're playing with a freedom, if you like. We're just looking forward to every game now."
Rooney has also returned to form in recent months, scoring seven goals for United so far this season in all competitions.