The Imps had to battle through tough conditions at Carlisle United on Tuesday night.
Chris Maguire's first goal for the club gave City a deserved lead at Brunton Park but despite dominating posession there was no second goal to put the game to bed.
The Cumbrians levelled through Jack Armer's second-half strike, and were victorious 4-3 in the penalty shootout.
The Imps were backed by 75 fans who made the long trip to Cumbria. Players Adam Jackson and Archie Mair, who travelled with the team but were not part of the matchday squad, rewarded two supporters at random to present signed shirts to.
Attendance: 884 (75 away)