The midfielder has allowed the likes of Ross Barkley to shine this season.
Martinez has infused his side with young stars since taking over in 2013, with the likes of Ross Barkley, Romelu Lukaku and John Stones developing under him.
This season has seen even more young talent take centre stage, with Brendan Galloway stepping up and Gerard Deulofeu shining.
However, it is the ageing Barry that is a mainstay in the team, and Martinez says his influence in the side is what allows him to trust his young players to perform.
“He [Barry] never panics and for our young players that’s very important," he told evertonfc.com.
“He is the most consistent footballer you are going to get in a dressing room. That’s down to his character.”
“I’ve said it many times - I always feel safe and confident of giving young players an opportunity because I know there are players like Barry, with know-how and experience, in the side.”
While Barry often comes in for stick from the Everton faithful, there is no denying the important role he plays in the side.
He struggled last season but has been in fine form this year, protecting the defence and helping to dictate the play.
That has allowed the side’s more attacking talents, namely Barkley and Deulofeu, to focus on doing just that and as a result, flourishing.
Martinez will be hoping that continues to be the case as they eye a potential Champions League place come the end of the campaign.