Republic of Ireland midfielder McCarthy joined the Toffees for £13million from Wigan in a last-gasp deadline-day deal last week.
Former Wigan boss Martinez has overseen much of the 22-year-old's development having first signed him for Latics in 2009.
The Spaniard sees McCarthy as a replacement for the departed Marouane Fellaini but he insists the fee paid will not dictate whether he is selected.
Martinez said: "Money is only the way you bring a player into a football club.
"James McCarthy has played over 100 games in the Premier League at the age of 22, he is a full international. The price comes through the market.
"Once you get into the dressing room it doesn't matter whether you come through the ranks like Ross Barkley or John Stones, or if you have paid a record fee. Everyone goes into the same situation.
"You need to work extremely hard to get in the team.
"That is what we want to create, real strong competition for places, where football can make the decision.
"I am delighted James McCarthy is here, I feel he has got the potential to be one of the best midfield players in European football.
- Sports & Recreation
- James McCarthy
- Marouane Fellaini