Kavanagh admitted he was still coming up the tunnel when Lawrence scored his first goal.
"I'm told it was brilliant," he said. "I ran the length of the field when he scored his second.
"It was a fabulous goal by Tom. He has quick feet and an eye for goal and he took it exceptionally well.
"When you start the way we did in those difficult conditions it's really good and we grew into the game.
"Our loan signings have adapted and done really well.
"I was very much concerned before the game, but we got the three points and the manner in which we did it is pleasing.
"Every time we went forward we looked dangerous and clubs in our league will start to take notice."
Teenager 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.