He has never regretted his decision and reveals how Martinez's powers of persuasion convinced him his future was at Everton.
Barry told the People: "It was how relaxed he was about everything.
"How he made me feel about my own game, what he thought of me, what he said I could achieve this season. It's easy for a manager to say those things but, sitting there and listening to him, I believed in everything he said.
"I'd seen the style of his teams and the way they played.
"I knew this was his first season at Everton, so it was a bit of a gamble. You weren't sure how the fans were going to take to him, how his style of play would work.
"Everton needed to change their style to fit the way Roberto wanted them to play, so you weren't sure how it was going to pan out.
"But the way he spoke to me, I believed in him and virtually every word he said to me has come true.
"In fact, everything has come true, apart from him saying I would get back in the England squad, which could easily have been achieved with different opinions."