The Hornets fought valiantly for 69 minutes before Brad Young fired the Blues in front. Zach Clough confirmed Carlisle's passage into the second round late on.
But who stood out for Horsham? Here are Sam Pole's ratings from the game.
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Action from Horsham's FA Cup first round clash at Carlisle United. Picture by Stu Forster/Getty Images
. Sam Howes - 9
Imperious between the sticks. The Horsham stopper made a number of key saves to allow the Hornets to stay in the game for as long as they did. Photo: Adam Nurkiewicz/Getty Images
. Steve Metcalf - 7
Good performance at full back, doing everything that was required to hold Carlisle off for as long as possible. Made a key header off the line to deny the Blues a goal. Photo: Steve Robards
. Jack Brivio - 7
Sturdy in the heart of the defence and his partnership with Miles kept Carlisle’s dangerous attackers quiet for 70 minutes. Photo: Derek Martin Photography and Art
. Will Miles - 8
Solid as rock at the back. Dealt with pretty much everything the Carlisle attack attempted to throw his way. Photo: Lyn Phillips & Trev Staff
5. Harvey Sparks - 8
Ran up and down the line and looked dangerous on the left-hand side. Made an excellent goal saving clearance off the line from a corner. Photo: Derek Martin Photography and Art
6. Charlie Harris - 6
Measured and composed in the middle of the park but mainly played as a runner as the hosts dominated possession throughout. Photo: Derek Martin Photography and Art
7. Tom Kavanagh - 6
Decent all-round performance in midfield and was dangerous when the visitors looked to break on the counter. Photo: Stu Forster/Getty Images
8. Lee Harding - 7
Constant thorn in the side of the Carlisle defence trouble down the right-hand side with his running, and almost took the lead for the Hornets but his header went just over the bar. Photo: Derek Martin Photography and Art