Town were roared on by more than 5,600 travelling fans in their gutsy FA Cup defeat at Liverpool on Sunday and Cotterill noted a recent trend in their vocal support.
Montgomery Waters Meadow also boasted one of the biggest league attendances since the move to the stadium as more than 8,200 piled in for the most recent home and league fixture, the 1-0 victory over Sheffield Wednesday.
Cotterill's men were also well backed in their Boxing Day win at Fleetwood, where Salopians enjoyed celebrating three unanswered goals for their side's first away League One win of the season. Another boosted figure is set to follow Town on the short away day venture to Crewe as Shrews return to league action on Saturday.
"I was really proud of the boys, the dressing room, the football club, the supporters behind the goal – tremendous – they've been like that for a little while now, really, really strong," said Cotterill.
"I think there were a few people going away on Sunday (impressed with us) – even Liverpool fans the way they were when we went off the pitch.
"You can't come away from there not thinking it's a special place."
Sunday's FA Cup third round gate at Anfield has been confirmed as 52,226 and nobody of a Shrewsbury persuasion will forget the moment Daniel Udoh stunned the Reds with his 27th-minute opener.
Some fans have said taking the lead on Merseyside, which lasted seven minutes, was among the wildest moments following the club and likened it to James Collins' opener at Arsenal in the League Cup in 2011.
Town have been allocated just over 1,000 tickets for the short trip to Gresty Road on Saturday. Hosts Crewe are struggling this season and sit second-bottom ahead of a home clash against Charlton, who are level on points with Salop, tonight.