The 19-year-old defender is yet to start a Premier League fixture, but has impressed the coaching staff at Goodison Park since completing a January switch from Barnsley.
He was hardened to the demands of senior football during his time at Oakwell and is being tipped to have a bright future in the top flight.
Martinez will have no qualms about throwing Stones into action when required and believes he will benefit more from time spent working with the Everton squad than from a short-term stint elsewhere.
Of the England U21 international, the Toffees boss told the Liverpool Echo: "I think he can develop here fighting for his place.
"He's earned that and I don't think he needs to go out on loan and play. Here he is learning on a daily basis from Jags (Phil Jagielka) and (Sylvain) Distin, and that's exactly what he needs.
"He's not the same player from pre-season, he's already gone to a different level.
"He's got an incredible future which we're all excited about and we're looking forward to him fighting to see how quickly he can get in the team.
"Every player is an individual and needs different things.
"John has had first-team experience. He played enough with Barnsley in the Championship to know what to expect."