The youngster was back in the starting line-up for their FA Cup draw with Chelsea.
Moyes said: "Jack's got real competition with (Marouane) Fellaini, (Mikel) Arteta and sometimes Leon Osman in there. We've got Tim Cahill to come back as well.
"To get in our side is difficult, especially in midfield. Jack has come in and performed well.
"He is progressing really well for a young lad and has a big future in the game."