The 45 million euro signing made an encouraging debut for the Red Devils at Old Trafford on Tuesday but his manager says the club still has much room for improvement.
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The Premier League champions remain six points behind fourth-place Liverpool, and Moyes is keen for his squad to improve further in its bid to secure a Champions League berth.
"Don't think because I have won tonight I'm smiling and happy. With the vision I have got for the club we have got a long way to go," the Scot told reporters.
Juan Mata made his debut following his 45 million euro move from Chelsea, while Wayne Rooney returned from a groin problem to make an appearance off the bench against Cardiff.
But Moyes maintains the England striker and Van Persie will remain as a strike partnership in the wake of Mata’s arrival.
"I can play him [Mata] in any role. Left or right allows me to keep the Robin and Wayne partnership. I'm quite comfortable with that," said the United boss.