England international Barkley, 20, starred on his comeback from a two-month layoff as the Toffees recorded just a second Premier League victory of the season.
Everton manager Martinez has insisted that he did not rush the midfielder back from the knee injury that had previously prevented him from playing this campaign, and admitted that his performance left him astounded by his natural ability.
"He played with the group this week and he was phenomenal, " Martinez told reporters. "You watch and just wonder if he was born to play football.
"As humans you are not born to kick a ball but he looks more natural with a ball at his feet than without it. When you looked at some of his movement on the ball, especially early in the game, it just looks like he was born to play football.
"There was no medical risk in starting him, the only worry was how long he could last. He lasted longer than I thought but he looked as though he had been playing all season. He was sensational in that respect."