The Town manager and his staff were extremely unhappy with a decision not to award Luke Leahy a late penalty after the Town man's heels were clipped in the hosts' penalty area.
Cotterill also argued that the corner which led to Macauley Bonne's winner should not have been awarded, insisting Elliott Bennett let the ball run behind as he knew it was a goal kick.
The away manager felt the 19,000-plus home crowd influenced the game's big decisions on a day where Shaun Whalley's screamer, which pulled Town level at the break, in the end counted for nothing. Cotterill and assistant Aaron Wilbraham raced over to the officials at full time for an explanation.
Cotterill said: "Once lads go back out (after half-time) you need a couple of things to go your way.
"We certainly don't feel it was a corner, we know we've got to defend the corner better, but if it's not a corner then it's not a corner.
"Elliott can keep that in play, so why would he let it roll out if it wasn't a corner? We wouldn't do that, we could keep it out or get a throw-in.
"It's not a corner and it's happened twice this season, the crowd have got them back in the game today, they've put pressure on the referee and he's ended up buckling on that.
"They buckled when it was a penalty and we don't get a penalty, there's no coincidence with that being at their end.
"I'm not sure but, just looking at the camera angles you've got, it looks a penalty to me.
"Luke Leahy says his shinpad has caught me. When he's being that specific, I trust Luke. I ask them to give me the truth so when I come to you guys I'm not telling you a bare-faced lie.
"We feel really hard done by with that, but that's what happens when you come away to a big club, those fine margin moments, when they don't go your way, we end up losing the game 2-1 when we haven't deserved to lose the game."
A third league defeat on the spin leaves Shrews down in 23rd in League One, having played as many as two games more than some rivals.
Cotterill said of his side's display, in which the visitors ended the first half the better team: "It was probably patchy. I thought we were very well organised up until they scored their goal and then we haven't defended a cross very well.
"They've ended up with a free header for the (first) goal and Marko makes a save and they get the rebound, we're not happy with that part of the first part of the game.
"Other than that we thought we got to a stage where it was almost like they were running out of ideas even though it was that early in the game.
"We were quite happy with our start, getting into the game, it was almost like when they scored it kickstarted us again with a real good goal by Shaun and we go in at half-time.
"We're slightly disappointed with the goal but we needed to do more of the same in the second half and we've not manged to do that.
"I felt the midfield lost a little bit of the shape in the first half that worked so well, not that any of them did anything bad, but it wasn't quite as tight or organised."