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."
Everton head into the clash having lost only once at Goodison Park this season in all competitions, and with eight straight victories in front of their own fans.
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