Barkley has had a breakout season for Everton with four goals in 21 appearances in all competitions, while he also made his senior international debut for England in September.
The 20-year-old attacking midfielder is expected to be part of England's World Cup squad to go to Brazil and Martinez believes Barkley has a level of technique and control on the ball that is decidedly un-English.
"He [Barkley] has the physical elements of the British game, the intensity and the power," Martinez told reporters on Friday. "But Ross also has the touch of someone brought up in a different culture.
"Nothing fazes Ross. That temperament, I'm not sure we've seen that too often over the years."
Martinez went on to explain that he thinks a serious injury changed his young star for the better.
"For some reason, the English talent is often the naughty boy. It's a short fuse or he gets into some kind of trouble. Drinking, smoking," he said. "Ross is the opposite. I think partly because he had a big injury at 17 [when he broke his leg in three places].
"All of a sudden something took it all away from him. He realized what he could lose. But home is good too. He's well grounded. His mum is a great influence. He's one in a million."