The Spanish boss, who arrived at Goodison Park as David Moyes's replacement in the summer, has kept faith with the 20-year-old, who has put in a number of impressive performances for the Toffees so far this season.
"I knew when I heard Martinez was coming in I'd get my chance this season," Barkley told the Liverpool Echo. "I'd seen the way he was with Callum McManaman and James McCarthy at Wigan, that he gives young players their chance.
"I knew I was the type of player to suit him because he's a really tactical manager who likes to build up the play. So I felt confident this could be the season I'd break through."
Martinez has stated today that the midfielder is yet to sign a new deal.