City were defeated in the first game of their EFL Trophy group as Derby County won 2-0 at Pride Park.
Derby enjoyed more of the possession early on, and had the first shot of the game when Korey Smith tested Jordan Wright from 20 yards.
Elliot Embleton then tried his luck from range after a quick counter-attack from the Rams, but his effort sailed over the crossbar.
A corner from the right was powered over by Sonny Bradley as Derby continued to push for an opener.
The hosts almost took the lead just before the break when a mazy run down the right from Kane Wilson resulted in the full-back finding Louie Sibley in the box.
Sibley took a touch, but his finish was wild, with the ball spiralling over the crossbar.
After the break the Rams continued to push, with Barkhuizen skying a chance after he was set up in the box by Wilson.
City almost pounced at the other end with Joe Wildsmith denying Jovon Makama from close range.
In the 51st minute the Rams took the lead through Tom Barkhuizen, with the winger finishing from James Collins’ threaded through ball.
Louie Sibley arrowed an effort over from 20 yards in the 67th minute as the hosts searched for a second goal.
Derby doubled their lead in the 77th minute when Nathaniel Mendez Laing’s deft touch took the ball into the path of Sibley who finished high into the net.
The Imps almost reduced the deficit when a corner found Ted Bishop unmarked at the back post, but his downward header was cleared off the line by a covering defender.
Ethan Hamilton then aimed to replicate his strike against Carlisle as he forced Wildsmith into action with another long-range strike.
Wright made a fabulous save in injury time to deny the Rams a third with Mendez-Laing curling an effort towards the top corner.
Derby: Joe Wildsmith, Kane Wilson, Sonny Bradley, Eiran Cashin, Callum Elder, Tyrese Fornah, Korey Smith, Elliot Embleton, Louie Sibley, Tom Barkhuizen, James Collins.
Goals: Barkhuizen (51'), Sibley (77').
Imps: Jordan Wright, Jaden Brown, Jack Burroughs, Alex Mitchell, TJ Eyoma, Jay Benn, Alistair Smith, Oisin Gallagher, Dylan Duffy, Hakeeb Adelakun, Jovon Makama.
Referee: Sebastian Stockbridge.
Attendance: 2,726 (251 away).