Town left with a share of the spoils in their 400-mile round midweek trip to Kent where 140 brave Shrewsbury souls braved the Arctic conditions to see their side struggle against the side who started the evening bottom of League One.
The visitors enjoyed their best attacks in the first period and went closest when a scrambled effort appeared to drop over the line before Gillingham's Max Ehmer intervened with his arm, but referee Brett Huxtable had already blown for a foul on goalkeeper Pontus Dahlberg.
Elliott Bennett's free-kick was Town's other best chance to claim three points and only shot on target.
But managerless Gills, under the caretaker stewardship of Steve Lovell after Steve Evans' departure, came on strong after the break and had the better openings towards the end as Danny Lloyd, Olly Lee and Charlie Kelman all went close.
Cotterill, who named the same starting line-up for a seventh game in succession, introduced defender Aaron Pierre on the hour and sent for new boys Saikou Janneh and Tyrese Fornah with 15 minutes remaining. He felt, however, a number of players could have been withdrawn after below-par evenings.
He said: "We just had too many tonight that have been brilliant in that starting XI (recently) off-colour, I'm not being funny I could've changed probably nine of them at half-time.
"It's what happens, we haven't been like that for a little while. Whether the losing goal at the weekend can affect you a little bit in the manner it has happened.
"They might use a lot of emotion in it and coming out of it with nothing it's important in the next game you don't get beat and we haven't done that, we have that to build on."
Fornah, the midfield loan signing from Nottingham Forest, came on from the bench alongside Bristol City loan frontman Janneh.
Cotterill said: "I've done that to please you guys so at least you can have a look at them now and stop asking me questions 'when they are going to go on the field and when they aren't and how fit they are?'
"They did alright, it was an awkward game to come into, but they are where they, they are where they are regards their fitness and their understanding of everything."
The Shrews boss – whose side climbed to 17th with a point, was cryptic in his response about any further incomings in the January transfer window, with less than a week until the deadline. He has previously said he is still looking for another couple of additions.
"It's a bit misty at the moment, I'm still looking through it," he joked. "I've got my Chamoi leather out at the moment trying to wipe it down to see what I can find out for you as soon as I know anything."
Gillingham had 13 shots and three on target to Town's four and just a sole effort to trouble Dahlberg.
The Shrews manager reserved praised for the hosts, who climbed to 23rd.
"We had to defend at times. It's always a difficult game when you come away to Gillingham, they put it in your box from the first minute," Cotterill said.
"You've got to make sure you defend your box, that's what type of game it's going to be when you come here.
"Steve (Lovell) has taken over for a couple of games now, I actually think they'll get better between and the end of the season. He does a really good job whenever he takes over the team. I think he does a good job and would be a difficult game coming here under Steve.
"It didn't end up being a very good game of football to watch, but we were fantastic on Saturday but ended up getting nothing, so thank small mercies at least we got a point out the game.
"It's a long journey and now we've got to get home and ready for another long journey on Saturday (to AFC Wimbledon)."
He continued: "The first half had our better opportunities to score. When we're getting into those areas, it's difficult to comment on what happens, but we've had scenarios where we've got in that area and when you have Elliott Bennett on the ball there aren't too many better.
"He normally picks out the right pass, delivers a great cross, I remember a few moments on Saturday.
"They seem to be getting cut out, so that'll be something we look at in more detail on the way home on the bus.
"They said before they've got three home games against sides in and around them, they wanted nine points but they're not getting three off of us, that's for sure."