The midfielder also says he is looking to add more goals to his game, starting with Manchester United this weekend.
The Blues have enjoyed a strong start to the 2015/16 campaign, sitting seventh in the table after eight games, with 13 points from a possible 24.
There have been several draws in that period, though, despite them dominating games, with the recent stalemate with Liverpool and a 0-0 with Swansea earlier in the campaign obvious examples.
And McCarthy has called on the Toffees to raise their game and ensure one point becomes three on a more regular basis.
“It’s a decent enough start but, as the gaffer says and each and every one of us knows, we need to try and pick up more points and get a bigger tally,” McCarthy told evertonfc.com.
“The other week against Liverpool, they controlled the first 15 to 20 minutes and then we went on and got stronger, especially in the second half when I thought we really dominated at times. The few points we have earned away from home, we could have sneaked a win maybe and turned one point into three.”
On a personal level, the Republic of Ireland midfielder has admitted that manager Roberto Martinez wants him to start adding more goals to his game.
Despite having made 86 appearances for the Blues since joining in 2013, McCarthy has only managed to find the back of the net three times so far.
And while his manager wants him to offer more in the final third, he insists that the most important thing is that he does his job in the side, which is to protect the back four.
“Within our style of play, he [Martinez] wants me sitting in at times but the last few weeks he has said to me to try and get forward as much as I can,” he added.
“But the most important thing is me doing the team job. My job is to work hard and protect the back four. I need to try and add goals to my game. There’s a few things I need to add - shooting and stuff - but I’m still learning the game.”