The 19-year-old has missed just three minutes of Everton's unbeaten start to their Premier League campaign and his form has seen him rewarded with a place in Roy Hodgson's England squad for the World Cup qualifiers against Montenegro and Poland next week.
He made his full England debut a month ago after coming on as a substitute against Moldova, with the Capital One defeat to Fulham his only real rest so far this term.
But Martinez is confident Barkley can handle the step up in responsibility for club and country.
"Ross is upset even when he can't win in training, never mind when he can't be involved in games," said the Spaniard.
"He is a young man who has been waiting for this opportunity for a long time and is desperate to enjoy every single second.
"When you are young you don't feel tired. He has a terrific energy and it is just the start of what is going to be a very special season for him."
Martinez was impressed with the speed with which Barkley and Romelu Lukaku struck up a partnership, as evidenced in Monday's 3-2 win over Newcastle.
"You see good players always understand each other. I thought Ross and Romelu clicked in the second half of the West Ham game and have developed in training a bit of a natural understanding of each other's game," he said.
"You are talking about 20-year-old players who excite you for the future.
"Their potential is terrific and we have to keep working and developing them because they are an important part of our team now.
"You can always work on certain aspects of the player but normally it is a natural relationship that is allowed to develop.
"Good players always get to know each other well in the way they enjoy their football. It is something which they can grow and improve in the future."