The 19-year-old midfielder impressed at Arsenal on Tuesday when he came within inches of breaking the deadlock and improving Everton's outside prospects of Champions League qualification.
Barkley could get another opportunity at Sunderland on Saturday with Leon Osman struggling with a groin problem but, having missed more than a year of football with a triple leg fracture, the England Under-21 international must be handled carefully, according to his manager.
"Ross has a long way to go and you should not expect to see him regularly," Moyes said. "If I think he is the best man for the job he will definitely play but we have had a lot of good players in the middle this year. I will play him when it is right.
"When he started at Tottenham we did not have [Marco] Fellaini or [Steven] Pienaar, the other night we did not have Ossie [Osman]. When he has got the opportunities he has to do it and he did well the other night. Are we having to find a role for him? That is something we have think about."
Barkley has spent time on loan at Sheffield Wednesday and Leeds United this season to gain the experience he missed while sidelined and Moyes believes rough edges remain. "There has been a lot of stuff said about him this week because he came in, he done OK and better than against Tottenham," Moyes said.
"I hope he is better again next time. He has a lot of maturing to do and needs to make sure he does not lose the ball in the wrong areas of the pitch. I can see he has got confidence from the Arsenal game and hopefully that will help.
"We have to bring him along and hope we get him better over the next year or two. If you're dropping your shoulder and losing it at the edge of their box it is not a problem but if you're doing it at the edge of your box then it is a problem. They are the sort of things he has to come to terms with."
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