Town were the better side in a competitive goalless affair at Gresty Road, where the visitors could not reward the near-1,500 visiting fans with a winner to remember.
A point helped Salop extend their unbeaten league run to five games, while they have not conceded in four League One contests. Cotterill felt midfielder destroyer Davis, 30, was everywhere for his side.
"I thought David Davis was our best player, for 90 minutes I thought he was outstanding," said Cotterill, whose side remain 15th.
"I'm on about from the first minute to the 93rd minute, he didn't change.
"He was our driving force in the first half, Digga, and to be fair to the other boys they joined in with him a little bit more in the second half.
"Then it makes it a good team performance, they don't feel they want to let each other down."
An eye-catching display was the latest in a series of performances from experienced former Birmingham man Davis, who has shone since returning to the side from suspension last month.
Cotterill has named the same unchanged XI for five games running and also acknowledged that will not go on forever.
He added of Davis: "I think that's fair. Maybe the goal (against Cheltenham at home on return from suspension) gave him a good boost.
"With 10 men that day it was an awesome performance by him. The good thing about it is the squad is getting stronger and we need that.
"That's really important because this team won't be able to keep going and going, something will happen where someone takes a dip and I'll have to take them off, give them a rest and have a look at it again, then they will ready to go."
Shrewsbury are set to add more competition in his department, with Cotterill this week looking at completing a loan deal to provide his midfield trio with more depth.
Fellow experienced Town star, wing-back Elliott Bennett, was another impressive performer in Cheshire as the visitors almost snatched maximum points late on through Matt Pennington and Ethan Ebanks-Landell headers.
Bennett said: "I think we did enough to win the game, chance-wise especially, but another clean sheet and point keeps our little run going with another home game to look to next.
"The travelling fans were great, it's a shame we couldn't send them home with three points. But it's a positive result.
"I just tried to do my bit for the team, we work on things in the week, playing in the (wing-back) system you're required to defend and provide things for forwards and midfielders to score goals."