Five consecutive league victories have set up a tantalising clash at home to Arsenal which, if they win, would take Everton within a point of the fourth-placed Gunners with a match in hand at home to Crystal Palace.
While a top-four finish is far from assured McCarthy admits the incentive could not be more evident for players now as they look to avenge their FA Cup quarter-final exit last month.
"Arsenal at home is going to be a big one," the Republic of Ireland international told evertontv.
"I'm sure the fans will come out in their numbers, hopefully we can put things right from last time we played them and push for that Champions League spot.
"They put us out of the cup and it is never nice to get beat. 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 in front of us, we can go and give it our best shot.
"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 to be fair."
Manager Roberto Martinez thinks his side, who have progressed significantly in his first season in charge, have learned much in the last couple of months.
"I don't think it goes down to the cup game (against Arsenal), if I'm honest I think it goes a little bit further than that," the Spaniard told the Liverpool Echo.
"We had two outstanding performances (both ending in 1-0 defeats) against Spurs and Chelsea and couldn't reflect that in the scoreline.
"It was a real focus of the group to learn from that and a maturity to know how to affect scorelines when you play well.
"It's fair to say in the last five league games we have not been fantastic in every game but we have found a way to be competitive and know what to do during the game and make sure the results have been positive.
"We are delighted with the return of points at this stage of the season and we have another 21 points to fight for.
"We have four fixtures at home and we are very excited about that.
"We know Arsenal are a phenomenal side but we will give it everything we've got and the support of our fans will make a difference."