The £13million summer recruit from Wigan made his home debut in Monday's 3-2 win over Newcastle and put in an assured performance.
"I still need to keep my head down and keep working hard. It still comes down to a day-to-day basis," said the 22-year-old.
"With Gareth (Barry) alongside and Ross (Barkley) in front I really enjoyed it."
McCarthy's partnership with Barry, on-loan from Manchester City, is likely to be key for the Toffees this season and manager Roberto Martinez has already seen positive things from the pair's work.
"I thought James McCarthy had a terrific partnership with Gareth Barry and that pleases you a lot," said the Spaniard.
"It allows you to build a good future for the football club."
Barry is ineligible for this weekend's trip to face parent club Manchester City as Everton's unbeaten record, the last remaining in the Premier League, goes on the line at the Etihad Stadium.
However, McCarthy believes the form of their other on-loan player Romelu Lukaku, who has scored three goals in 135 minutes of football, gives them hope as they look to hold on to fourth place.
"Romelu was different class (against Newcastle)," he told evertontv.
"Now we just need to kick on. The unbeaten record is still going and we are gelling as a squad and long may it continue.
"You want to be up there and challenging but it is never easy."