Rory Loy bundled home what proved to be the winner a minute before half-time and eight minutes after Akpa Akpro saw red for kicking Carlisle defender Frank Simek.
Tranmere threw everything at the Cumbrians after the break but found keeper Mark Gillespie in inspired form while Liam Palmer had a goal ruled out for offside.
"Jean-Louis Akpa Akpro is a vital part of this team but he has let everybody down," said Moore.
"You just can't do what he did.
"He has kicked out at an opponent and now he is banned for the next three games. Some of the decisions were not good from the referee but he had no option with the sending-off.
"And if you are going to get promoted you have to take your opportunities. We need to put the knife in but we have committed football suicide in the first half.
"There was no spark from us in the first half. We showed spirit, desire and commitment after half-time but we didn't get that bit of luck we needed.
"The crowd got behind us and that is the tempo we need to play at but the sloppiness of the first half cost us. We have to win as a team. If players go missing then we are in trouble."