Town had to settle for a Montgomery Waters Meadow point despite taking the lead for the first time in 10 games this season through Sam Cosgrove.
Crewe's ex-Town man Mikael Mandron netted an equaliser on the stroke of half-time and it was the Railwaymen who looked the more likely in the second half, as David Artell's side passed up several key chances.
Cotterill was content with the effort and defending on show from his troops today, given the boss admitted his players are still in a 'strange' place following a difficult start to the campaign.
"I think probably, if we had defended their goal from the front better, it could have been three points, but on the day it was a hard fought game and a draw ends up being a fair result on the day," Cotterill said.
"It was pleasing to score first for the first time, it was just a pitty that we didn't get another to build on that
"It is difficult for the lads at the moment because they are in a strange place, they are young lads who don't always know what to do in those moments, but we showed character today.
"In the second half at spells we had to defend our own box well, their team grew bigger and ours grew smaller, they put big balls in the box and caused problems.
"We put in fantastic tackles and blocks, and at the end it was no different to our defending last season. I don't think we have defended as well as we did today in and around our own box.
"The goal on half time is never a good goal to concede, any goal is tough to take. We re-grouped after that and I think the lads defended well today."
Mandron and his Alex team-mates missed several more chances to notch a winner in front of a boisterous away end. Town's best chance to claim all three points came through a header from substitute Ryan Bowman.
Town defender Aaron Pierre came off late with an eye injury in which he found his vision was blurry for five minutes before being withdrawn.
Even 10 minutes of stoppages could not settle the breathless contest, which finished in a 'ding-dong' manner, according to the boss, in front of an edgy Meadow.
Shrewsbury's search for a first clean sheet of the new season goes on and stretches one game into last term. While Cosgrove's 19th-minute opener did, at least, end a nine-game run of opponents scoring first in games this season.
The boss, whose side moved up to 21st with the point, added: "When a game gets to 80 minutes and it becomes ding-dong on a boiling hot day, you're always fearful because you don't want one to go in your net.
"But we had a couple of chances, I haven't looked at the Matthew Pennington penalty shout yet, but a few people seem a little bit convinced, but I don't know.
"But I think, with some of the decisions today, they got the rub of the green, I'm not sure we got the rub of the green on a few decisions.
"There's been a lot of work done on all aspects. It's been a tiring week for myself and the players.
"With what's gone on, with the preparation and hard work, it'd been a real travesty today if we'd have got beat, a real kick in the teeth.
"It is a step in the right direction (a draw) when you're getting beat, isn't it? I'll be looking forward to you guys saying we've moved up a place, we take all those small gains at this moment.
"We'll carry on working, we've got a good group of lads, supportive chairman, and fanbase that got behind the lads again today, so I thank them. We'll keep on working."