Pools trailed 3-1 with nine minutes remaining after goals from Taylor Charters, Manasse Mampala and Tristan Abrahams cancelled out Matty Daly’s first half strike.
But a fine goal from Luke Molyneux and a penalty from Fela Olomola forced a penalty shoot out which Carlisle won 4-3.
That sees Pools take a point away from the game while The Cumbrians claim two in the group stages.
Scroll down and click through the pages to reveal the Pools player ratings from the game…
1. Jonathan Mitchell - 6
Made a number of confident claims and saves but will be disappointed with Carlisle's second goal. Photo: HUFC
2. David Ferguson - 5
One of only two Pools players to keep his place in the side from the weekend. Wasn't as effective as he was on Saturday. Photo: Bernadette Malcolmson
3. Timi Odusina - 6
Almost scored an early own goal but recomposed himself and put in a few decent challenges. Photo: Mark Fletcher
4. Luke Hendrie - 5
Thrown straight into the starting line-up after signing yesterday. Held his own despite a lack of gametime. Came close to scoring a debut goal with a header from a corner too. Got forward well when needed in the second half too. Photo: Pete Norton