"To get compared to players of that calibre makes me think I must be doing something right on the pitch," Barkley told the Liverpool Echo on Thursday.
"I don't really think about it that much but it's nice to hear.
"I've watched videos of Gazza on YouTube when I was growing up - one of him against the Netherlands in Euro 96 when he was class, so I know what type of player he was. And obviously I watched a lot of Michael Ballack.
"It's mad because the way Martinez says I'm like Ballack, my Sunday League manager used to say that when I was 11."
His performance against league-leaders Arsenal again raised expectations around the Liverpool-born player, with England fans hoping he will play a major role for the national side at next year's World Cup in Brazil.
Barkley joined Everton at 11, making his league debut in 2011 before loan spells at Sheffield Wednesday and Leeds United, and made his full England debut this year against Moldova.
He said he when Martinez was appointed as David Moyes's replacement earlier this year he was confident he would get the opportunity to play regularly given the way the Spaniard promoted young players while in charge of Wigan Athletic.
He was happy with his progress, but having netted twice this season, was keen to increase his goalscoring tally.
"Like any player there's loads of ways I can improve," he said.
"I want to score more, but I'm young and I know I'm going to score plenty more.
"I want to be creating more chances too and contributing assists because in my position that's something I've got to be able to do."
Martinez told reporters ahead of Saturday's clash with Fulham that Everton, sitting fifth in the league, were looking to offer Barkley a new contract.
"You can imagine we're always working behind the scenes to try to reward youngsters that do really well at the club," he said.
"Ross is clearly that.
"But there's nothing to announce. The moment that we do have something to announce, the fans will be the first ones to know. Even when you don't speak about issues, we work really hard behind the scenes to make sure the youngsters get rewarded and Ross deserves that."
(Reporting by Josh Reich, editing by Justin Palmer)
