The Blues boss was keen to praise the influence the midfielder has on his teammates.
The midfielder has enjoyed a strong start to the season with the Toffees, after enduring a disappointing campaign last year, and was instrumental in their impressive 6-2 win over Sunderland on Sunday.
That appearance took him to 573 in the Premier League, making him the player with the third most appearances in the division behind Frank Lampard and current record holder Ryan Giggs.
And Martinez has likened him to the Welshman, saying that he can match the Manchester United legend’s longevity.
“Those players (like Giggs) are a very special breed, not just because of the natural element but also the lifestyle and the way they live the game,” the Daily Mail reports him saying.
“Football is a passion and Gareth is that type Everything he does, he does for a purpose, the way he trains is as a leader, he is an inspiration to the other players and he could go on and on and on until the body has enough.”
The Spanish manager was also keen to praise the effect that Barry has on those around him in the Everton team.
The midfielder is very much a key player in the Toffees side, with him having formed a strong partnership with James McCarthy in the heart of the midfield that has proven key to Martinez’s side.
His influence is also seen elsewhere though, as he allows the more creative players, such as Ross Barkley, the freedom to attack without worrying about their defensive duties.
That was evident in their big win on Sunday, and Martinez has backed Barry to continue playing that role in the Premier League for a few more seasons yet.
'He is a very, very fit footballer, but he plays with his brain and his technical ability allows the others to be effective around him,” he added.
“Clearly, he can play for a few more seasons at the level he is playing. Gareth is enjoying his football and is a very important football man.”