Shrewsbury have repeatedly conceded costly late goals this season but this time they managed to see the game out with goals from wingers Jon Taylor and Paul Parry, who volleyed in a 64th minute winner.
Liam Noble had pulled Carlisle level in between but Shrewsbury defended manfully to preserve their advantage.
"The players were sat in the dressing afterwards wondering just how they haven't got something out of the game," said Abbott, whose men have won only one of their last eight league games. "They're desperately disappointed.
"Generally on the road we have performed, we've got a good record, but there have been times this season we haven't performed.
"We can't believe how we've got nothing out of a game that we think for large parts we've dominated.
"I can't recollect too many times our goal has been under siege but I can talk about the other goal being under siege."
Despite the setback, Abbott stressed he was confident Carlisle's results would soon start to pick up.
"The performance, the energy and the determination will lead us into better things," he added. "There's no question about that.
"I'm disappointed because I can't believe I'm walking away from here as a manager who's got nothing out of a game we needed something from."