Since the Spaniard took over from David Moyes during the close season, Barkley has become a first-team regular at Goodison Park, making nine starts in the Premier League.
The 19-year-old's impressive performances have resulted in a call-up to Roy Hodgson's England squad.
Martinez is not surprised by Barkley's quick rise to international level and believes he has attributes that set him apart from other British talents.
"Ross is a really talented footballer," Martinez told talkSPORT. "As a British player he is as talented as anyone you see.
"The balance he has with both feet is brilliant, and technically he’s really gifted. You would see that technical ability with any Brazilian or Dutch player.
"He's a young man though and we need to allow him to fight through the normal process, which is gaining his first-team place and making sure he enjoys his football. At the moment he is doing that.
"I've been impressed with Ross’ personality and character; he’s such a humble boy, all he wants to do is listen and play.
"It’s such a simple case with him. Nothing will phase him on a football pitch and, if you’ve have a talent like his, it’s an incredible combination."
