The England international had yet to play this term after picking up a knee ligament injury during pre-season, but he enjoyed an eye-catching return to Premier League action on Saturday.
Everton cruised to a 3-0 win over Paul Lambert's side thanks to goals from Phil Jagielka, Romelu Lukaku and Seamus Coleman, with Barkley providing an assist for the Belgian forward.
Martinez acknowledged that he had little expectation that Barkley would be ready to feature against Villa, making the 20-year-old's performance even more startling.
He said: "The truth is, eight days ago in my mind he was nowhere near [being fit] - there was no option of him starting the game.
"In the last seven days he has been working, with the benefit of the international break, working individually and with the group and he was phenomenal.
"Sometimes you ask yourself if he was born to play football. As human beings we aren't born to kick a ball, but he looks more natural with the ball than without it.
"The way he trained I had no doubts. There was no risk from a medical point of view, the only worry was how long he'd last and he lasted longer than I thought he would.
"But if you look at some of his movement on the ball early in the game, it looked like he had been playing in every game this season.
"He has a phenomenal knack. He was sensational."
Everton had endured a disappointing start to the season after winning just one of their opening seven Premier League fixtures.
But one highlight has been the form of forward Steven Naismith and, although he did not add to his tally of four Premier League goals on Saturday, Martinez was once again immensely impressed by the Scotland international.
"I was worried about Steven because he had two demanding games with Scotland," he said. "Probably not playing full 90 minutes against Poland allowed him to be fresh today, but it was an incredible performance from him.
"I was delighted just to see the standing ovation he got from the crowd. He has been at that level for a long time now.
"He is such an intelligent player and he carries that desire to win which is infectious. He shows how important he is for the team and I was delighted to see how he handled the need of playing three games in such a short period of time."
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