Carlisle teenager Tom Lawrence, on loan from Manchester United, struck in each half and his sublime efforts were added to by David Amoo and James Berrett before Ryan Lowe grabbed a late consolation header for Tranmere.
Moore said: "Despite conceding after about 30 seconds it was wide open at half-time and could have gone any way.
"But we were gutless in the second half - as bad as I've seen since I was manager.
"We were mentally and physically weak. When I put them out I expect them to roll their sleeves up and fight.
"We've lost 4-1 to Carlisle who are in a similar position to us. That's nine goals conceded in two games and there's not a great deal you can do.
"It is soul destroying for me, the players, the supporters and the club. I expect a bit of heart and desire and we didn't have that, which is disappointing to me.
"As a group of lads there's not enough passion and pride in the Tranmere shirt.
"It was a wide open game and we needed a goal to come in at half-time, but we self destructed."
Lawrence, making his first league start, stunned Tranmere with a brilliant first-minute strike from 25 yards and his second half solo goal was even better - a mazy dribble before firing left-footed across keeper Owain Fon Williams low into the bottom corner.
Lawrence impressed with his powerful shooting in the first half when Carlisle won a free-kick all of 35 yards out. Fon Williams was glad to parry a bullet of a shot, which came through a crowd of players.
Amoo made it 2-0 in the 52nd minute, lashing home Berrett's corner on the volley from eight yards out - the former Tranmere forward's eighth goal of the season.
Lawrence produced a goal of the season candidate in the 67th minute before Amoo's dash down the left flank set up Carlisle's fourth, a fierce drive from just inside the area by Berrett.
Carlisle took their foot off the gas late on and Lowe pulled a goal back for Rovers in the 81st minute with a far-post header.