Town put in arguably their finest display of the season to claim a deserved share of the spoils with a 1-1 draw at Hillsborough, where they made it unbeaten in nine league games at Sheffield Wednesday.
The visitors were roared on by up to 1,000 travelling fans as striker Ryan Bowman marked his return to the starting line-up with an equaliser before half-time after Saido Berahino headed the hosts into an early lead.
Cotterill's men benefitted from Owls talisman Barry Bannan's first-half penalty miss as Wednesday passed up a number of early openings.
But Shrewsbury were extremely comfortable in a second half in which their hosts struggled to create much of note other than a disallowed goal for offside. Town went close to sealing a memorable win but left wing-back Luke Leahy sent his effort narrowly wide of the far post.
"We could've nicked it really when you think of some of the chances we could've had," Cotterill said when asked about his side's performance.
"Luke Leahy shot went wide and I thought that was in all the way. When you come to a place like Hillsborough, with the size of the crowd they've got, you sort of fear the worst.
"We didn't start the game with enough belief, I believe, then we did grow into the game.
"But to be fair I think we could've won the game in the second half."
There was some contention as Berahino headed in Bannan's corner after just six minutes but Cotterill confirmed a corner should not have been given.
The boss, however, revealed his disappointment as his side shipped another goal from a set-piece, and feels something has been 'lost in translation' in Town's struggles in that department.
He added: "It shouldn't have been a corner, their lad has kicked it out, it's not a corner.
"We haven't regrouped quickly enough from that.
"I just said in there – normally and before I came in we are good at defending corners. My teams are predominantly good at defending set-pieces, because we work on them.
"Something seems to have got lost in translation, I just said to the boys, we're giving away cheap goals to team. That's something we need to be better on all round.
"But great character from the lads to come back and, as I said, could've won it at the end."
Bowman bagged his first Town goal and a first in League One for the 29-year-old as he scrambled home at the near post following neat build up.
The experienced summer recruit returned to the starting line-up for youngster Tom Bloxham after a period out of the side with a hamstring injury.
"It was a real poacher's goal, a little toe-poke getting it over the line," Cotterill said. "I thought he was excellent today, Ryan Bowman, I'm really, really pleased for him.
"I'm pleased he's got off the mark and that might give him that extra belief after the hamstring injury he had, which he's never had before.
"I thought he was excellent, his physicality, great fitness levels, I'm really pleased."
The boss, who confirmed Olamide Shodipo's second-half goal was correctly adjudged offside, added on his side's win: "I think in the end they'd have had more possession from us but I think we had more efforts at goal, I don't know that, but I'm trying to replay the game back.
"Hopefully, if you can come to Sheffield Wednesday and get a result and stick them on the back foot for periods in the game then there's no reason why we can't go anywhere else and do it.
"Maybe that's what they've needed a little bit, hopefully that's the case."
Cotterill's troops were roared on by their biggest away following of the season so far and, just like their side, the travelling army out-shone their hosts, particularly in the second half.
No official number of away fans was given but Town had shifted 850 tickets by Friday and, even though trouble on the M1 meant some fans arrived late, the visiting Salopians backed their side all afternoon, even after a difficult first half hour.
Cotterill said: "The amount of fans we had, the travelling fans were absolutely first class today.
"A big thank you to them, because travelling in those numbers and supporting the lads today was brilliant."