The Republic of Ireland international, who signed for the Merseyside club in a £13 million deal from Wigan moments before the transfer window closed in the summer, has begun his Toffees career with a string of outstanding displays.
McCarthy is already a fans favourite at Goodison Park and Martinez believes there is more to come from the midfield stalwart.
"He is one of those players you watch and say, 'He fits so well in that football club'. There is a real love for that type of midfielder. The Evertonians see James as the midfielder they would pick and like," said the Spaniard.
"He has that urgency to get the ball back, but also shows composure and style on it. He is still only 23 and the amount of games he has played in the Premier League is unheard of.
"He is still a young man and he can improve and get better. That is probably his challenge for the season, to be able to maintain that level that he has."
Although McCarthy has yet to score for the Blues, Martinez is not worried and feels the goals will come as he develops as a footballer.
"The role I play him in is stopping him from doing that. He is capable of getting 10 goals a season later in his career."