Jones, meanwhile, could be in contention to return in the Champions League at Bayer Leverkusen on Wednesday, a game Marouane Fellaini will miss through suspension.
"Kagawa got injured playing for Japan," Moyes said at his post-match press conference. "It’s an injury to his foot; there’s some bruising there, but it’s not too bad.
"Robin’s groin is the problem at the moment; his toes are much better. We are hoping to get both Nemanja and Robin back as soon as we can.
"I hope they'll be in contention for Wednesday but I couldn’t give you a definitive answer."
When asked if Jones could feature in Germany, Moyes added: "Possibly. I don't think he is as bad as we first thought. He's not too far away. It's a groin injury, right up his hip."
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