The 24-year-old, who netted six goals in 20 league appearances last season, made his first Premier League appearance of the campaign in the shock 2-1 loss to Steve Clarke's side.
His return to top-flight action was cut short, though, as 18-year-old Adnan Januzaj replaced him at the interval, but Moyes suggested that the change was tactical.
"We want Shinji to feel that he's getting an opportunity to show what he can do," the 50-year-old Scottish coach said.
"Arguably, his best position may be number 10 but I think for Japan he plays in the same position we're playing him just now.
"So it's not something which is strange to him or not his position but there's a lot of competition here and what we want is the competition to push each other on to get performances and improve."
United's indifferent start has left them 12th in the table but their next test comes in the Champions League on Wednesday, when they face Shakhtar Donetsk in Ukraine.