A much-changed Town side, featuring 10 changes, were seen off 4-1 at Montgomery Waters Meadow by the in-form Imps, flying high in League One.
Cotterill, whose team are five points from safety in the League One drop zone, insisted the evening was about having a look and running the rule on his back-up squad members and the manager admitted he was 'hoping for more'.
Cotterill said that the heavy round of 32 exit opened his eyes to where the packed Town squad he inherited currently sits. He added that he now feels he has been on the right track with the side he has selected for league action.
Asked if the tie highlighted work that needed to be done in the upcoming January window, Cotterill said: "When you get a job and the team is down at the bottom, there's always a lot to do, so I'm under no illusions of that.
"Changing it overnight 100 per cent doesn't happen. This season will be one of those hard-working grinds to get out of where we are."
"I never want to get beat in any game. You can tell there are quite a few that are quite a fair bit behind.
"I needed to see the boys that I haven't really seen yet. I'm not sure it was a 4-1 game, there were a couple they'd got good blocks and we haven't for their goals.
"I just needed to have a look at a few lads tonight and this was going to be my only opportunity. If I had the opportunity again I would still do it - I needed to do that.
"I would say some did (impressed) and some didn't. They haven't played a lot of football, through injury, a lack of 90 minutes, it showed me tonight where the squad is.
"It's funny, when I think about where I got in that short space of time watching a few games (on video), to pick the starting line-up that has played in the league games so far. I think I'm on the right track with my thinking."
Lincoln led through Anthony Scully and Zack Elbouzedi before Shilow Tracey grabbed a goal back for the hosts ahead of half-time.
But Remy Howarth and a Jorge Grant penalty ensured Shrewsbury's exit from the competition.
"I was looking for more from everybody, certainly in the second half," Cotterill added.
"I have a better idea now of where our squad is as a whole, because you can't just work off the back of 11 players.
"There were some good individual performances but the trouble is they were only individual and not maybe part of the team.
"Shilow needs to work on other parts of his game for him to progress in his career.
"I was hopeful of more than that, tonight, yes. But they are perhaps at a stage when they can't give more."
"If they are not quite up to speed the pitch will find you out, because you've got to get about it. If you look at a couple of their goals they've come from counters.
"We've been alright in possession but we haven't been good on the turnover, which incorporates running back towards your own goal.
"I've said I'll find out who gets tired on recovery runs, everyone gets forward quickly but the recovery runs are not always as quick."