The Blues have taken just seven points from eight games and currently sit 21st in the Vanarama National League, without a win at home since December.
McCarthy was given his marching orders on Wednesday after a 2-0 defeat at ten-man Solihull Moors on Tuesday night.
Tom Shaw, Dave Felgate and Calum McIntyre have been tasked with preparing the team ahead of Saturday's game at home to Ebbsfleet United, with the search for a new manager underway.
Speaking about McCarthy's exit and the visit of unbeaten Fleet, Shaw said: "It's a sad time for us as staff and players, he did a hell of a lot for all of us. He's a terrific coach, a great ambassador for the club and a really good man.
"They've got some good players but we're not concerned about them this weekend, we're going to exploit all of our strengths and attributes within the squad to get the best out of it. It's my job for the next few games to get every grain of energy and ability out of them.
"Looking at the way the players have trained, they're going to work hard, be on the front foot and positive.
"The environment that has been set is top drawer. I think I'm going to have to change certain things just to try and find the spark within this group. I will tweak certain bits but nothing wholesale."