Graham Turner felt his side's anxiety proved costly as Shrewsbury failed to take the chance to widen the gap between themselves and lowly Bury to 11 points after a dismal 0-0 draw.
Chances at either end were few and far between although Shrewsbury did strike the crossbar midway through the first half when midfielder David McAllister's deflected 25-yard drive looped up against the woodwork.
"The performance was full of anxiety and I believe we're better players than we've shown," said Shrews boss Turner.
"We didn't create an awful lot. We had a little flurry just after the substitutions and with a bit of luck David's effort might have gone in instead of hitting the top of the bar.
"But generally it was just a battle out there and to be fair to our players, Bury set up with a very difficult formation to play against."
Bury boss Kevin Blackwell, who included three newly-signed loanees in his starting XI, was satisifed with the Shakers' efforts even though their winless run in all competitions now stands at a dozen games.
They almost snatched three points in the closing stages but an effort from Ethan Ebanks-Landell was scrambled off the line.
Blackwell said: "When you come away from home the first thing you do is accept a point, that's for sure, especially considering we've been training on a five-a-side pitch at the Trafford Centre for the last two weeks because of the weather.
"We've brought in Nicky Ajose, Ashley Eastham and Stephane Zubar this week and that team had never played or trained together before the game so I accept the point.
"We were very well organised and didn't allow them to build up any real momentum. From that point we were able to actually create the better chances."