Van Persie looked in severe pain when he went down in the 90th minute under a challenge from Kostas Manolas. He was stretchered off the pitch and went straight down the tunnel.
However, speaking to reporters in the post-match press conference, Moyes appeared confident the Dutchman would soon be back on the pitch.
"I don't think Robin's too bad," he said. "He's got a knock just behind his knee. We'll know more in the morning – we'll assess it – but he had a knock in the back of his knee. We hope it's not too bad."
Van Persie's hat-trick was his third since joining the club and the first by a United player in Europe since Michael Owen netted a treble against Wolfsburg in December 2009.
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