Roberto Martinez's men have moved to within four points of Arsenal in fourth with a game in hand on their London rivals, on the back of a five-game winning run in the Premier League.
The two sides meet on Sunday at Goodison Park in what could be a defining game in their seasons, and McCarthy feels that Everton are in great shape.
"Hopefully we can get a Champions League spot," the Republic of Ireland international told the club's official website. "It's going to be a big ask but we will give it our best shot.
"It's in the balance and if we want it, it's there for us.
"As a squad we believe we can do it but there is a long way to go.
"You need to enjoy the occasion and the challenge, if you don't then you are in the wrong game."
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