Barkley was a second-half substitute in England's recent matches with Lithuania and Italy, and his direct play earned plenty of plaudits.
The impact made by the 21-year-old came as no surprise to Martinez who, having monitored him closely at Goodison Park, believes Barkley could become a key member of England's squad in the future.
"He is used to having to deal with extremes," said the Spaniard. "When he is playing well he's called the best footballer in England, but when he has a bad game, it changes.
"What is true is that he has an incredible level of maturity.
"He's learned a lot having come through a serious injury and it doesn't surprise me that he made a good impact coming off the bench in both England's games.
"Ross is one who takes responsibility in big moments of games and has developed that physicality as well.
"There are not many footballers in Europe with the same level of ability."
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