Both players arrived at Goodison Park in the summer transfer window, with McCarthy joining from Wigan Athletic and Barry moving to Merseyside on a season-long loan from Manchester City.
"You need that blend of experience and youth and that partnership reflects it perfectly," the Liverpool Echo quotes Martinez as saying.
"You've got the know-how of Gareth and the legs, freshness and bravery of James. Their partnership is as good as it gets in that blend. Those two are at the centre of everything."
The Toffees are currently fifth in the Premier League table after 15 games.