City bowed out of the Emirates FA Cup despite a battling performance at Salford.
An even match could have gone either way and, in the end, was decided by a penalty shootout which was edged by the home side.
Erik Ring's first goal of the season had given the Imps the lead, but they were pegged back in the final minute of the four added on by referee Steven Copeland at the end of normal time.
Both sides had chances to nick it in extra-time - and the Imps finished 120 minutes having had more shots and more possession than their hosts, but it was Salford who went into Monday night's draw for the second round.
Head coach Michael Skubala made five changes, with Adam Jackson partnering Ryley Towler in the centre of defence. Jackson was returning from a groin injury, while Tom Hamer dropped out with a similar problem.
Ivan Varfolomeev came into midfield, partnering Conor McGrandles, with Freddie Draper and Erik Ring also coming into the XI in attacking positions.
The home side, confident after a start to the season which saw them third in the Sky Bet League Two table, opened brightly and forced George Wickens into a save in just the third minute.
Kallum Cesay took aim through a crowd of bodies from 25 yards. Wickens could have only seen it late, but did well to tip the ball over the bar.
Cesay impressed in the opening exchanges, and his cross for N'mai was dangerous - needing a vital clearance from Towler.
And Wickens needed to be alert after 18 minutes to prevent the home side taking the lead. The ball was well-worked by Salford following a corner, with Cesay and Kelly N'Mai involved before Grant's powerful close-range effort which was palmed away by the visiting keeper.
The Imps had seen off the early pressure, and started to look much more of a threat themselves. Ben House did well, sending a defender one way then the other, before seeing his low right-footed effort tipped away by the left arm of home keeper Mark Howard.
And only an intervention from Mnoga denied James Collins a shooting opportunity, after great work from Freddie Draper.
The opening goal, with 27 minutes on the clock, came after Ring picked up the ball from Darikwa inside his own half. He set off on a run down the right, getting past more than one defender before powerfully smashing the ball past Howard.
Ring saw a shot blocked by Cooper, before two stoppages of play due to injuries to Imps players which disrupted the pace of the game. House and Varfolomeev both needed treatment. House was replaced, with Rob Street coming off the bench, but Varfolomeev was able to continue - though Cesay was booked after his hefty challenge which saw the Ukrainian youngster left on the floor.
The Imps threatened from the free-kick awarded for Cesay's foul on Varfolomeev, with Ring's delivery flicked on towards Draper at the far post. Draper created space for a shot, but lifted his effort just too high.
The visitors controlled the match as half-time approached. Two corner deliveries from Reach were flicked on by Towler, whose flick-ons just failed to find a team-mate, while he also pulled the ball back for Ring who tried an effort from distance which flashed wide.
Street, who had played down the right wing after his introduction with Ring switching to the left, also saw an effort blocked as the home side dug in to ensure they were still in the game at the interval.
The opening contests of the second period were even, with Adebola Oluwu clearing the ball ahead of Collins from street's cross and McGrandles trying his luck form distance.
Karl Robinson made a triple change to try to get back into the match - sending on Fabio Borini, Kadeem Harris and Daniel Udoh after 53 minutes. That took his changes for the match up to four, having brought on Josh Austerfield to replace Cesay at the restart.
A free-kick just outside the D of the area gave the hame side a brilliant opportunity. Butcher's powerful left-footed effort was palmed upwards away from danger by Wickens, who then calmly collected the ball from the resulting corner.
Salford unsurprisingly enjoyed plenty of possession as we pushed for a leveller, with Ring getting in a vital block as N'Mai lined up a shot from outside the area and Udoh glanced a header wide from fellow substitute Harris.
N'Mai did have the ball in the back of the net from close range, after a dramatic overhead kick from Haji Mnoga sent the ball over to his direction. That moment, with 20 minutes to go, was a clear warning to the Imps that they could not take anything for granted.
Skubala made changes of his own as the second period progressed, initially sending Sonny Bradley and Lewis Montsma on after 66 minutes. Then, after 77 minutes, Tom Bayliss and Justin Obikwu entered the play.
That helped City regain more of the balance of play, with McGrandles again trying an effort from the edge of the area - but Howard again held the ball well.
Salford again had a free-kick, won by Harris, from a dangerous position right on the edge of the area. Borini lifted the ball over the wall with a right-footed effort, but it dipped over the bar.
Another great save from Howard denied Street in the 90th minute. The fourth official Oliver Bickle indicated four minutes of time added on and these were almost through when N'mai slotted the ball home after Udoh found a way to get the ball onto him.
That setup a further half hour of extra time. Bayliss was the first to threaten for the Imps, with a shot blocked behind.
The home side took their momentum from the end of normal time into extra time, with N'Mai getting a dangerous looking shot away which was deflected behind.
Darikwa did have the ball in the back of the net 1towards the end of the opening period of extra time, but the assistant's flag was up as City's skipper was offside when Reach played the ball over.
Darikwa was clearly well onside moments later when Obikwu found him with a low cutback but perhaps did not realise how much time he had as he tried to place the finish into the bottom-right corner but did not have enough power to trouble Howard.
Borini briefly thought he would win the tie for the home side, again profiting from the hard-working Udoh, but his low shot was held by Wickens.
The Imps were reduced to 10 men when referee Steven Copeland showed Darikwa his second yellow card of the match, after City's skipper went down in the area. Copeland felt that it was simulation, and the yellow card was followed by a flash of the red card.
Bayliss went agonisingly close in the final minute of extra time, getting away down the left before lifting a shot which just rolled past the far post.
And, as the seconds ticked away, N'Mai saw an effort blocked by Montsma onto the bar, and the tie went to penalties.
Although Wickens did get a touch to Ben Woodburn's penalty kick, City bowed out as the home side converted all of their set-pieces.
Street and Obikwu converted low penalty kicks for the Imps, with Bayliss seeing his effort come back off the woodwork and Howard blocking from McGrandles.
Salford: Howard, Cooper, Oluwo, Turton (Woodburn, 86), Longelo (Harris, 53), Cesay (Austerfield, 46), Butcher, Grant (Borini, 53), Mnoga, N'Mai, Stockton (Udoh, 53). Subs: Young, Butt, Carroll, Garbutt.
Imps: Wickens, Darikwa, Reach, Jackson (Bradley, 66), Towler, Collins (Bayliss, 77), Ring (Montsma, 66), McGrandles, House (Street, 37), Varfolomeev (Okoronkwo, 112) , Draper (Obikwu, 77). Subs: Pardington, Thorn, Lembikisa.
Referee: Steven Copeland
Attendance: 1,951 (794 away)