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.
"But the transfer fee will mean nothing. It means he is here now."
McCarthy has so far trained little with his new team-mates having been away on international duty with Ireland over the past week.
He has returned with a slight knock but is in contention, along with fellow new signing Gareth Barry, to make his debut in Saturday's Premier League clash with Chelsea at Goodison Park.
Barry also joined the Toffees on deadline day in a season-long loan from Manchester City.
A third new recruit, striker Romelu Lukaku, is on loan from Chelsea and is not permitted to play against his parent club.
On the prospects of McCarthy and Barry featuring, Martinez said: "They will be involved, I don't know in what way. It will depend on how they settle in.
"It is a real shame Romelu is not available. He has come back from his spell with Belgium really sharp and with a real desire to help the team.
"They are players with good experience and they are going to help the team."
McCarthy's Ireland team-mate Seamus Coleman also has a minor niggle following the latest World Cup qualifiers but otherwise Martinez has no fresh injury concerns.
Midfielder Darron Gibson and defender Antolin Alcaraz are both back in training but not yet ready to feature.
Gibson has not played yet this term after suffering a knee injury in Everton's final pre-season friendly against Real Betis last month.
Alcaraz, signed on a free transfer from Wigan in the summer, is still awaiting his debut as he recovers from a hernia operation.
Martinez said: "Darron and Antolin are in training with the first team.
"Now it is a case of getting the match fitness. That could take a couple of weeks, depending on how they react.
"Darron and Antolin won't be fit for the weekend but they are not going to be too far away.
"It has been a great couple of weeks for Darron, especially, in terms of getting really close for being available."
Everton have started their Premier League campaign with three successive draws.
Now the international break is over Martinez is pleased to be able to have his full squad together, including the new signings.
He said: "It's been a real joy to see Gareth Barry around, with his daily standards.
"James McCarthy hasn't been able to train with the group yet, Romelu has been with us a couple of days.
"It is always great to have new faces being integrated into the group.
"I don't think it has been a difficult time for any of those players.
"It has been a good welcoming period. We can't wait to get the full squad working together."