Shrewsbury boss Kevin Ratcliffe admitted his side will have to produce a better performance in the second leg if they are to progress to the LDV Final at the Millennium Stadium in Cardiff.
"We could have done a lot better," he said after the game. "We were sloppy and gave the ball away too much.
"Carlisle put us under lots of pressure and closed us down quickly but we started poorly and made it hard for ourselves.
"But it's only half time in this cup tie and we are 1-0 down and it's all to play for now. We've got a long way to go and if we play like that in the second leg we'll struggle." Carlisle boss Roddy Collins was downbeat about the United win.
"Shrewsbury look likely to be favourite to go to Cardiff now," he said. "They did a good job on the night keeping it tight but we should have scored more goals. That was not the side that will play us down there." Shrewsbury produced few real chances and have their defence and some woeful Carlisle finishing to thank for holding Carlisle to a single goal lead.
Shrews keeper Ian Dunbavin did well to save a Richie Foran penalty in the 18th minute awarded after Matt Redmile had been harshly judged to have fouled Stuart Green.
But four minutes later Carlisle were in the lead just as it looked as if Shrewsbury would go in front. Carlisle keeper Matty Glennon did well to steer a Darren Moss shot round the post and from the resulting corner a quick Carlisle attack caught the visitors napping.
Craig Farrell raced upfield to play the ball to Adam Rundle who did well to place his shot past Dunbavin and a defender.
Rundle said: "The pressure's on them to perform at Gay Meadow. It's a shame Richie Foran missed the penalty. They would have been more comfortable with a 2-0 lead but our defence was solid and I hope we can keep a clean sheet in the second leg. The main thing was to win here tonight."