The 22-year-old completed his transfer from Wigan late on Monday night, eclipsing the £9.5million Spartak Moscow paid for Republic of Ireland team-mate Aiden McGeady.
McCarthy says the fee will bring no added pressure and is delighted to again be plying his trade in the Premier League.
He said: "It's a new challenge and I am really looking forward to it. I have had a few people on my case about it, and it's one I'm going to need to take in my stride.
"Hopefully I can make the step up to a big club at Everton, and it's one I'm looking forward to.
"Obviously I am delighted to be back in the Premier League. It's a real excitement and a new challenge for myself."
McCarthy was given permission to delay his departure for Ireland as he attempted to tie up his move to Goodison Park, but even then he had to wait until the 11th hour.
"It was hectic," he admitted. "It wasn't nice to be waiting about, especially as it took until 10.50pm when we got confirmation that it was going to happen.
"It was just a relief, to be honest, and such an excitement to go to such a brilliant place like Everton."
You can see the Republic of Ireland's World Cup Qualifier against Sweden on Sky Sports 2HD this Friday at 7.30pm