Scott Murray was denied by the woodwork as City's second-half onslaught came to nothing.
The 18-goal winger produced a brilliant overhead effort in the 47th minute, but saw the ball cannon back off the crossbar.
It was the nearest Danny Wilson's team came to securing a first league win of 2003, despite camping in the Brentford half for much of the second period.
The visitors had a hero in keeper Paul Smith, who made fine saves to deny Craig Fagan and substitute Christian Roberts as his defence came under constant pressure.
The first half was a scrappy affair with plenty of effort from both sides, but little end product.
Fagan, on loan from Birmingham City, had the best two chances, shooting wide early on and being denied by one of several Smith saves shortly before the break.
Brentford made a half time substitution, bringing on Mark McCammon to partner Rowan Vine up front and switching Steve Hunt to the left of midfield.
It was Hunt who put in their best effort just after Murray had hit the bar but his low drive was saved by Steve Phillips at his near post.
Apart from a McCammon shot that was deflected wide, Brentford spent the rest of the game on the back foot.
City threw on strikers Lee Peacock and Roberts in the closing stages and both might have snatched victory.
A terrific 25-yard strike from Roberts was parried by Smith, with the City player firing wildly over from the rebound.
Peacock shot into the side-netting from a Tom Doherty pass as City's frustration grew in the closing stages.
Brentford will be far happier with the result although they are also seeking a first league win this year. It was a battling effort from the visitors, but Wilson will feel his side should have won at a canter with more composure in front of goal.