The Japan international has not yet featured for the Reds in the Barclays Premier League this season and was missing from the squad that saw off the Eagles 2-0 at Old Trafford.
Afterwards, Moyes confirmed at his press conference that the midfielder is recovering from an illness the manager feels was contracted on international duty.
"Shinji hasn't been in that much; he's been travelling back and forth between us and Japan," Moyes said.
"Today, it looks as if he's picked up ‘flu through flying so much and he's been tired. He trained yesterday and didn't feel great. We hoped he'd improve in the hotel overnight but he didn't, so there's no need for us to take the risk.
"We're trying to get him back but we've not had the chance to see him and he's not been here that often, so we've not had the chance."