United rounded off their Checkatrade Trophy Group A games with a home game against Fleetwood Town on Wednesday evening.
But two first half goals from the visitors left Carlisle with too much to do as they exited the competition at the group stages on what was a frustrating night of football, despite pulling one back late in the day.
An early cross from Devitt caused problems as it dipped late and had to be hooked clear by Cargill. It fell nicely for Lambe but his instinctive volley flew over the bar.
Fleetwood responded with some good pressure which gave Sowerby room to shoot. He went for it from 25-yards but it was always heading just an inch too high.
It was the visitors who took the lead on 10 minutes when Sowerby made a determined run into the box. He exchanged passes with Schwabl to create space and he caught George flat-footed with a drilled effort which crept into the bottom corner.
United had a chance to pull level almost immediately when a lobbed cross from Grainger was flicked on by Cosgrove. It bounced awkwardly inside the area, and Ekpolo misjudged the movement, and that left Devitt with a decision to make. He went for a first-time volley but he couldn't keep it down.
The Cumbrians came again with some lovely football as they picked a path through a packed defence, but Lambe was prevented from shooting by a timely tackle when he looked to latch on to a pull back from Devitt.
Things became tight, particularly in the midfield areas, but a misplaced pass from Grainger brought Schwabl forward. That was rolled into the path of the unmarked Godswill Ekpolo and George had to save with two hands as a stinging effort zipped through bodies and headed for his top corner.
It was good pressure from the visiting team and Schwabl was next to have a go with a volley from distance. That came off Jones and deflected behind for another corner. Cargill arrived late to meet that one but his header went high into the stands.
Shaun Miller took matters into his own hands as he tried to provide a spark for the hosts with a shot from nowhere with 25 minutes on the clock. His first touch stopped the ball dead and he was a whisker away with a shot from the angle which had Neal well beaten.
Carlisle enjoyed some good spells of possession ahead of the break and they almost unlocked the door on 36 minutes when Brown swung a cross to the near post. Shaun Miller got in front of his man to glance it goalwards but it flew past the upright.
The Blues stayed forward and a well-worked corner routine gave Jones the room he needed to deliver. It was met on the full by Tom Miller but his 14-yard header went like a bullet over the bar.
Sam Cosgrove did well with a lovely long ball from Tom Miller as he took it down on his toe with just Neal to beat. Cargill arrived just in time to nick the ball away. It was all about Carlisle and Shaun Miller was disappointed when another good pass fell at his feet. He kept it close but leaned back and ballooned his effort into the night sky when the chance to shoot came his way.
The Carlisle domination was made to count for nothing as a lightning quick break brought Ekpolo forward. He used pace to get to the edge of the box and his pass inside invited Biggins to shoot. George did well to get a hand to it, but he could do nothing as Burns followed up to nod the loose pieces into his net.
Parkes had a header cleared off the line by Schwabl in time added on for the half, and Grainger curled a 23-yard free kick just over as the Cumbrians walked down the tunnel knowing they had plenty to do.
Fleetwood had a real scare at the start of the second period when a cross from Jones was met by Rodgers as Neal scampered off his line. The pair got in a real mix but keeper Neal recovered just in time to claw the ball off his line before Devitt could force it over.
United peppered the box with crosses through another dominant spell, with Devitt and Shaun Miller pulling wide to provide the ammunition, and Grainger won a corner when he rattled a first time cross at Neal from a tight angle. That was well delivered by Devitt but it was allowed to bounce untouched across the face of the target.
Lambe crunched one wide from distance as Carlisle kept trying to find a foothold, and Neal spilled a dangerous Grainger corner and had to be rescued once again by a goal line clearance as the United strike force watched in hope that it would go into the net.
The Cumbrians stayed on the front foot and a neat pass from Devitt brought a spin from Shaun Miller on the edge of the area. He spotted Neal off his line but his shot went the wrong side of the upright once again.
Another corner somehow made its way through everybody without finding a touch until Lambe tried to recover it at the back stick, but Carlisle had to concentrate at the other end when Schwabl found a raking pass to put Nirennold clean through. His first touch was heavy and George was quickly out to scoop it up.
Cosgrove was thwarted by a good save from Neal as United sent more men forward in the closing stages, and the keeper was on hand again to deal comfortably with a free kick from Grainger.
The Cumbrians were handed a lifeline with six minutes left to play when a determined run from Brown brought a rash challenge from Maguire. Grainger stepped up to take it, but his first and second efforts were blocked. Shaun Miller stayed alert and he was on hand to stab it in from very close range.
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Goals
Carlisle United - S Miller (84)
Fleetwood Town - Sowerby (10), Burns (44)
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Bookings
Carlisle United - Devitt (32), T Miller (55)
Fleetwood Town - Biggins (29)
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Teams
Carlisle United - George, Brown, T Miller, Parkes, Grainger, Lambe (Rigg 77), Jones (Joyce 66), Devitt, Etuhu (O'Sullivan 66), S Miller, Cosgrove. Subs - Bonham, Liddle, Hope, Nabi.
Fleetwood Town - Neal, Burns, Maguire, Rodgers, Ekpolo (Nirennold 69), Schwabl, Nadesan (Donohue 74), Biggins, Sowerby, Sheron, Cargill (Higham 46). Subs - Crellin, Hunter, Baines, Kerrigan.
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Referee - Martin Coy
Attendance - 909 (42 away fans)
