The Blues' last piece of silverware was the 1995 FA Cup and last reached a final when they lost to Chelsea at Wembley in 2009.
Despite being unable to compete financially with their rivals, the Toffees have consistently hovered in around the Champions League places, but McCarthy has wants to see the side pick up a trophy this season.
The Irish midfielder enjoyed a fine debut season at Goodison Park last term after his £13 million switch from Wigan Athletic, but the former Latics man wants to build on an encouraging campaign by winning silverware this coming season.
Speaking to the Liverpool Echo at their pre-season training campaign in Austria, McCarthy said: “We want to go and win things. This is a fresh start, a long season, and one that we are all looking forward to. There are a lot of games and a lot of competition, but we want to win things."
McCarthy also revealed that he is looking forward to getting restarted after shaking off an ankle injury that ruled him out of the Republic of Ireland's post-season friendlies.
"I had a nice summer, pretty chilled,” the 23-year-old added. “I pulled out of the Republic of Ireland squad because my ankle had been bothering me. [ROI Manager] Martin O’Neill was OK with it.
“For me, it was good to get a break in. I enjoyed my summer, but now it’s back to work. I’m looking forward to getting started again.
“I think the rest will make me a lot fresher and a lot fitter. I had a niggle with my ankle, and that has given it time to heal. I feel a lot fresher than I did at the end of the season.”
Roberto Martinez's side begin their Premier League campaign with a trip to newly-promoted Leicester City.