The Bees had won five league games in a row but they drew a rare blank against Graham Turner's hard-working side.
Shrewsbury might even have pinched it but winger Jon Taylor's shot midway through the second half was headed off the line by defender Harlee Dean with goalkeeper Richard Lee beaten.
Marcelo Trotta, on loan from Fulham, twice failed to hit the target with presentable chances at either end of the first half, but in between Shrewsbury were the more dangerous side.
Darren Jones headed just over and Marvin Morgan's flick from a Matt Richards free-kick drifted narrowly wide before right-back Connor Goldson drove agonisingly off target from the edge of the penalty area.
Shrewsbury's work rate ensured Brentford never had any time on the ball to impose themselves.
The Bees were brighter after the restart and Trotta's deflected shot after a strong run was brilliantly kept out by consistent goalkeeper Chris Weale.
Adam Forshaw also fired just over in stoppage time for the Londoners but Shrewsbury, who have lost just once in their last eight games, deserved some reward.