Rovers lost only their third home game of the season as Carlisle left Prenton Park with all three points.
The sending off of Jean-Louis Akpa Akpro before half time cost Tranmere - with the visitors scoring soon after and holding on for a 0-1 win.
Rovers were reduced to ten men on 36 minutes when Akpa Akpro was ordered off for kicking out at Frank Simek following a tussle for the ball on the left wing.
Manager Ronnie Moore said the referee was right to show the player a straight red.
He said: "What a stupid thing to do. He'll be fined, he's let everybody down today.
"As good as he is, you can't have that. We all pay for one stupid lack of professionalism.
"The referee had no option."
Commenting after the game on Rovers' website, Moore said: "The first 45 minutes was unacceptable.
"We've spoken about tempo and turning them and for some reason in the first half we were kicking 60 and 70 yard balls which is not us. We pass, pass and then turn them.
"We're top of the league, but we can't turn up with seven players.
"We're not Manchester United, we can't get scrape a 2-1 win. We have to have eleven men up and at them, closing down and stopping people from playing. We never had that in the first half and it was comfortable for Carlisle."
Liam Palmer thought he had finally scored his first goal for Tranmere on 72 minutes when he turned a free kick against the post and followed up by firing in on the goal line.
But as he ran away to celebrate, the assistant referee raised his flag for offside.
Moore said: "We turned up in the second half and give the ten lads a big pat on the back. The offside was very close.
"In the end we nearly clawed something out of a disaster, but at least we showed some heart in the second half."
Rovers remain top of League One with 56 points and stay ahead of second-placed Doncaster on goal difference, but Doncaster have a game in hand.