Martinez believes that Barry, 32, is an Englishman playing a foreign No.6 role and that there is no one else who comes close in that position born on these shores.
He said: "Many times you get called the unsung hero but any team needs someone who has the understanding, the knowhow and who gives you the balance in the side.
"Gareth has been that and more because he's been creative. He's been incredible.
"He has always been in the middle of the good things we have done and he has been a clear example for the all the youngsters at the club like James McCarthy and Ross Barkley.
"His level of performance has been at the highest, highest level.
"I really enjoy watching Gareth going about his role at the club.
"His performance against Manchester United in midweek was as good as it gets for a midfielder in that sort of role.
"He had the hardest role in the game, which is controlling the United threat then allowing us to be imposing in possession.
"He is one of the best midfielders in the Premier League. He's been very influential in everything we want to do.
"I have always found it very difficult to find that No.6, that defensive, tactically aware midfielder in the English game.
"Historically, England has produced very good midfielders but they are box-to-box. They play in a different way.
"Gareth has developed that continental approach in his midfield role and I think that's quite unique.
"That's why I value Gareth so much. To have an Englishman with the approach of a continental midfielder gives you a really good advantage for other players to learn from.
"I really value what he brings to the club.
"Maybe Gareth would be more appreciated elsewhere if he was a foreign player.
"Sometimes it's not a glamorous thing to be English in that role.
"At the moment I don't think there's another English midfielder of his type who can bring what he brings.
"We have never lost a game with Gareth on the pitch and Roy Hodgson is well aware of Gareth and has been following his progress."
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