A Kane Hemmings brace sandwiched in between a goal from defender Rhys Bennett saw the Blues start the new year with a loss, despite Jamie Devitt’s penalty.
Mansfield led 2-0 at half-time.
Former Rangers man Hemmings opened the scoring with nine minutes on the clock, before Bennett tapped home his second goal of the season from close-range after United’s loan goalkeeper Jack Bonham had saved Lee Angol’s initial effort.
Blues boss Curle brought on strikers Richie Bennett and Hallam Hope at half-time as United switched to a 4-4-2 formation, with the changes making a positive impact.
Midway through the second period, Carlisle halved the deficit. Bennett was adjudged to have been fouled by home keeper Conrad Logan with Irish midfielder Devitt slotting into the bottom corner from the spot.
Bennett and and Sam Cosgrove both missed great chances to level the scores in quick succession with the pair both hitting the woodwork with around 15 minutes to play.
And, not for the first time in the game, the Stags cashed in on a Carlisle miss as Hemmings steered home Alfie Potter’s delivery for his second goal of the game.
“We made basic errors and we need to improve,” Curle said.
“If the players cannot improve, then maybe we need to look at changing personnel.”
On United’s glorious double opportunity which saw Cosgrove glance a Hope left-wing cross on to the post, before Bennett hit the bar from close-range with the rebound, manager Curle said: “At 2-1, there was only one team in it.
“Sam Cosgrove did well to get his head on Hallam's cross and then Richie’s hit the bar with the rebound. Two minutes later, they scored at the other end. Goals do change games.”
Midfield duo Luke Joyce and Kelvin Etuhu were both not involved in the squad.
Curle added: "Kelvin is having a scan today. He took a whack on Saturday in the final seconds of the game and is wearing a protective boot.
“We’re hoping he will be available soon.”
United host Championship side Sheffield Wednesday in the FA Cup third round on Saturday.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here