Everton currently reside sixth in the standings, eight points off a Champions League spot with a game in hand on the Gunners.
"To be honest, we have never written ourselves off in the Champions League," The Express quotes McCarthy as saying. "We will give it our best shot. We have got eight points between us and Arsenal and we have a game in hand, Arsenal to come here.
"It's still open. They will know they cannot let their standards slip. They will be looking over their shoulder now. They will be a bit worried."
The two sides will go head to head at Goodison Park on April 6.