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
13. Tom Richards - 6
Replaced Metcalf with the Hornets trying to secure an equaliser but ultimately couldn’t affect the game in the visitor’s favour. Photo: Stu Forster/Getty Images
14. Lucas Rodrigues - 6
Brought into midfield to try and create something but, with the hosts coming into life in the second half, found it hard to stamp his authority. Photo: Stu Forster/Getty Images
15. Chris Smith - 6
Came on late into the game but didn’t really have enough time to affect the game in a meaningful way Photo: Steve Robards
16. Danny Dudley - 6
Good performance after coming on. Unfortunate that the deflection off him wrong-footed Howes for the second goal. Photo: Stu Forster/Getty Images