The Republic of Ireland international has featured in all three of the Toffees' Premier League fixtures this season, scoring one goal in the process.
Having impressed for Everton during his five years so far at Goodison Park, Martinez believes that the 25-year-old is only getting better.
"He just grows month by month. He is a good example of a footballer with an incredible attitude and appetite for the game," the Spaniard is quoted as saying by BBC Sport.
"I haven't done anything to coax that out of him. He knows his potential. He plays in a demanding position which needs you to be so good in many areas. He's one of the best full-backs in world football."
Everton return to Premier League action on September 13 when they make the trip to West Bromwich Albion.