The 1-0 loss meant Salop finished 12th in League One on the completion of the 46-game campaign.
They could have finished 10th had they gotten the better of the Imps and Charlton lost to Cheltenham but it was not to be.
Town skipper Luke Leahy rattled the outside of the post in the opening exchanges, and Chey Dunkley also went close with a header.
Steve Cotterill's side were more threatening in the opening half of football. They had more possession and more goal attempts but they did not get the important lead.
The game followed the same pattern after the break, with Rob Street hitting the bar before Jordan Shipley fired straight at Carl Rushworth when through on goal.
Cotterill's men were punished with just under 20 minutes to go when Matty Virtue fired home from close range.
Town had comfortably been the better team, but they were not ruthless in front of goal.
The Lincoln opener took the sting out of Shrewsbury, and they did not look like getting back into it.
Dunkley was then sent off with little time left for fouling Ben House, and the referee pointed to the spot. Marko Marosi produced a wonderful save to keep it at 1-0 which is how the game finished.
For the final time this season, Steve Cotterill named his starting XI for a League One clash.
And it was unchanged from the team that got a battling 2-1 victory over Bristol Rovers in midweek.
Four Salop loan players were potentially in the team for the final time at Sincil Bank Stadium.
Carl Winchester, Street, Killian Phillips and Taylor Moore started and Christian Saydee who has been battling with injury was fit enough to make the bench.
The ground stood to sing the national anthem before kick-off due to the King's Coronation being this weekend.
Leahy hit the bar for Shrewsbury in the opening stages when a corner fell to him at the back post, it was bobbling around in the penalty area, and he unleashed a powerful effort which hit the outside of the post.
Moments later Town almost led again - another set piece - Elliott Bennett with a deep ball to the back post and it was met by Dunkley.
The defender did well to beat his man in the air but his header forced a wonderful save from Imps keeper Carl Rushworth.
It was persistent Town pressure. Shipley put a wonderful cross in for Killian Phillips only for the midfielder to head over from eight yards out.
They continued to probe, seeing the majority of possession in what was a really promising opening half an hour for Cotterill's men.
The Imps did come into it more as the half progressed, but without creating anything in the way of a meaningful chance.
Town went close again on the stroke of half-time, Rob Street did well to win a free-kick on the right side, it was whipped in by Bennett. Dunkley got his head to it first again but it went harmlessly over the bar.
Salop were by far the better team at the break - but they had no goal to show for it.
Street hit the bar for Town within minutes of the re-start after he got his head on Moore's cross but Rushworth was there to tip it onto the bar.
More good play from Street saw him play in Shipley, he had just the keeper to beat but he hit it straight at Rushworth and it remained goalless.
Just past the 70-minute mark, the Imps had their first chance worthy of mention. Matty Virtue had a volley from distance and it stung the palms of Marko Marosi in the Town goal.
But moments later they were ahead. Virtue found some space in the Town box and fired beyond Marosi.
Town had their chances, did not take them and were punished as a result.
It could have been doubled when House had a great chance to add a second, but his effort was cleared off the line by Moore.
In the closing stages, Dunkley was sent off after hauling down House. The referee pointed to the spot but it was saved by Marosi but there was no time to launch a comeback.
Salop: Marosi (GK), Leahy (C), Moore, Winchester, Phillips, Bowman (Bloxham 81), Street (Saydee 85), Bennett (Pyke 81), Dunkley, Shipley, Flanagan.
Subs: Burgoyne (GK), Bloxham, Craig, Barlow, Saydee, Pyke
Lincoln City: Rushworth (GK), Poole (C), Boyes, Jackson (Roughan 45), Shodipo (Sander 56), Erhahon, O'Connor, House, Sorensen, Virtue, Duffy (Makama 66)
Subs: Long (GK), Sanders, Plange, Eyoma, Roughan, Makama, Gallagher