The midfielder is on a season-long loan from Manchester City.
"I've been a big admirer of Gareth over the years," Martinez told evertontv. "He senses danger like nobody, gives you composure and is full of good decisions. He establishes good relationships with players all over the park.
"He is very unique because his type of midfielder doesn't normally exist in English football. You get a lot of foreign players coming in and playing that role really well but Gareth Barry is something else.
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