The Spaniard believes the teenager, currently on international duty with England, possesses technical skills on a par with Brazilian or Dutch contemporaries.
Barkley, 19, has become a key player in the side since the change of management at Goodison Park in the summer and Martinez is keen to progress the youngster's development.
"Ross, since day one, showed he was ready and in a position to enjoy his football and it is not a secret he is a really talented man," the Toffees boss told talkSPORT.
"Technically he is really gifted and you would probably see that technical ability in any player brought up in Brazil or Holland - he is that exquisite technically.
"He is a young man who is fighting for his place and his personality and character means he is such a humble boy, all he wants to do is listen and play.
"Nothing will faze him on a pitch and if you have that with the talent he has, it is an incredible combination."
Everton's good start to the season has put them sixth in the Barclays Premier League, three points off second-placed Liverpool ahead of this weekend's Merseyside derby at Goodison.
Martinez is still trying to implement changes in his playing philosophy and believes further progress will be made this season.
"We are better now than we were in August and in February we have to be at a better level," he added.
"The goalscoring ability of a team is very important. You are going to be successful in a season if you are solid defensively and have a threat of scoring goals.
"Scoring goals will come more often once we get the understanding of the players.
"We have goals in the side, I'm not worried about that. The focus is on the strikers but it is the wrong focus."
Source: PA
Source: PA