Ted Bishop scored a stunning goal on his first Imps start but it was not enough as City bowed out of the Carabao Cup despite an impressive performance at Shrewsbury.
New signings Hakeeb Adelakun and Bishop were handed their first starts for the club, and the latter impressed as he got his first goal for the club.
Bishop smashed the ball into a top corner from outside the area to add to Tom Hopper's opening effort as the visitors controlled most of the match in Shropshire - enjoying almost 60% of the possession over the 90 minutes.
They tested Marko Marosi in the Shrews goal as early as the fourth minute with Anthony Scully getting a free-kick on target after Bishop had been fouled.
Bishop went close with a smart finish after 12 minutes when a good move down the left saw Adelakun play him in, but again Marosi did well to keep him out.
The visitors were playing with swagger now, which was again evident as a one-two between Hopper and Scully ended with the latter forcing Marosi into yet another low stop.
Josh Griffiths was called into action for the first time after 26 minutes, after Bowman got a shot away from the edge of the area.
Adelakun sent a low effort wide from distance, while Cohen Bramall saw a free-kick hit the defensive wall.
There were no changes for either side at the break, and the Imps went ahead four minutes after the restart.
Bramall crossed the ball into the area and Hopper was on hand to glance it into the back of the net with his head.
Bishop made it 2-0 three minutes later with an unstoppable shot which left Marosi with no chance as the ball swerved away from him.
The Shrews pulled a goal back after 69 minutes. Griffiths was unable to hold a shot from the left and Daniel Udoh - on as a substitute four minutes earlier - scrambled the ball home.
Udoh was causing a real nuisance and he rifled in a leveller 10 minutes later with a shot into a bottom corner which left Griffiths with no chance.
That prompted a frantic finish to the match - with both sides going for it, albeit without too many clearcut chances.
There was late drama in time added on as the Shrews thought they had scrambled the ball over, only for Griffiths to make a great block on the line.
Regan Poole sent a late header over for the Imps, but ultimately the match was decided by penalties.
Griffiths did well to tip a Josh Vela kick past a post, but it proved in vain as Marosi also pushed a Lewis Fiorini effort aside and the Shrews claimed a 4-2 shootout win.