Lincoln boss Mark Kennedy claimed Shrewsbury were the better team after Ethan Hamilton earned the Imps a 1-0 victory.
The recent signing from Accrington struck his first goal for the club to stretch their unbeaten league run to three games.
Shrewsbury were the more dominant of the two sides and went close to breaking the deadlock on the half-hour mark.
Dan Udoh played a creative ball over the top to Taylor Perry, who cut inside and darted into the box but Lukas Jensen blocked his close-range effort.
The travelling side grabbed a late win after new-boy Hamilton tucked away from inside the area in the 79th minute to get his first goal in a Lincoln shirt.
Kennedy said: “It wasn’t a brilliant performance by us. For those that were not here it was really tough conditions, like incredibly windy and blustery, and it was really tough for both teams.
“Where I was really pleased was our grit, determination, togetherness and unity, especially of the back of Tuesday, which was so nearly a really good performance.
“But unfortunately, because they scored two late goals, you then get loads of questions which I get but to respond like that with a clean sheet which is three in five games.
“Strikers win games – they say – and defenders win titles which we are some way away from that – to make clear – but my point is that clean sheets are so important.
“I thought they were the better side but if you look at the chances, they have had two shots on target, and we only had three, but Lukas (Jensen) had a quiet afternoon as you get.
“The one chance that they did have was huge. I wouldn’t say it was a game changer because it was so early.”
Shrewsbury boss Matt Taylor said: “It’s a disappointing result but our first-half performance was good.
“We weren’t ruthless enough and when you are on top in this league, and in any league really, you have got to score.
“We missed too many good chances where we made the wrong decision too often in their box.
“And when you do that, and you don’t score when the momentum is with you, then you always risk this type of result.
“Speaking to the players at half-time, I wanted them to win the half out of possession and we didn’t do that.
“When you also play against teams of Lincoln’s quality, and you look at the 1-0 wins they got away from home last season, we always knew that whoever scored that first goal would win.
“To go in at half-time 0-0 with the chances we created and how comfortable we were in possession, I was really disappointed but ultimately we have not taken our chances.”