The 18-year-old, who is expected to sign a new long-term contract this week, made his Barclays Premier League debut in the Toffees' opening defeat of the season at home to QPR.
Barkley is highly rated at the club and although the player is desperate for more first-team involvement, he accepts he will have to be patient, telling Evertonian magazine: "It can be [frustrating] because I want to play all the time but I fully understand because I am still only very young and the manager knows what he's doing and what's best for me."
Moyes has never been reluctant to give younger players a chance, having brought through the likes of Wayne Rooney and Jack Rodwell.
And Barkley added: "He's had young players coming through before.
"That's what's great about Everton; the manager will always give young players the chance to play at the right time.
"I think I'll play in the FA Youth Cup this season, which will be useful."
Source: PA
Source: PA