The Toffees are currently four points behind fourth-placed Arsenal with a game in hand. However, they will be able to close that gap to one point on Sunday if they beat the Gunners at Goodison Park.
McCarthy believes that he and his teammates are good enough to seize the opportunity and take a step closer to reaching next year's competition.
"Hopefully we can get a Champions League spot," McCarthy 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 have won their last five matches in the Premier League.