The new manager began his Red Devils reign with a shock 1-0 loss to Thailand All-Stars on July 14 but registered his first win with a 5-1 triumph over A-League All Stars, in which the striker scored after coming on as a late substitute.
Van Persie notched 30 goals in his debut season at United, with Moyes underlining his importance to the squad on Friday, and does not expect any drop in form from himself or his team-mates under the new regime.
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"It’s a huge challenge to all of us and it’s one we’re looking forward to. Everyone wants to be successful. Moyes wants to be successful. He’s been working very hard and he’s spoken to every single player individually.
"It’s his first couple of weeks so let’s get to know each other. It looks very good. Moyes is very nice. He works very well. It’s only based on a few sessions, but I loved them."
The 29-year-old admitted there is a new feel to the club following Sir Alex's retirement, but says the team must concentrate given their rivals' improvements over the summer.
He continued: "It’s different. Of course it was a great season last time. It was my first year with him and the first year at the club I had with him. It was a great year for the club and we all did great things together.
"But now it’s a new year and I’m very much looking forward to it with a new manager and great new staff. For now we have the same players. Last season we won the league and that was great, but this time we want to win the league and more as well.
"We have to improve to stay ahead, because over the last few years the English league has become better and better. Every single team has got harder to beat. When you go away you have to perform 100 per cent otherwise you may lose."