Bees were keen to maintain their push towards the top after suffering a first defeat in 20 games against Wolves last week, but an injury-hit Carlisle deserved their share of the spoils with a point to keep them clear of the relegation zone.
In a first half which produced few chances, Brentford's leading scorer Clayton Donaldson posed the main threat to a makeshift Carlisle defence and went closest with a shot from just outside the area which fizzed past the left-hand post.
Bees played a neat passing game, which gave them plenty of possession, but it was Carlisle who finally managed to test Bees goalkeeper David Button in a lively spell after the break when he had to keep out efforts from David Amoo, Liam Noble and Brad Potts in quick succession.
Brentford pushed forward in a bid to break the deadlock and Marcello Trotta just failed to turn a cross in from close range before Alan Judge hit a stinger of a shot from 25 yards which home goalkeeper Jordan Pickford parried at full stretch.
The second half was a big improvement on the opening 45 minutes and Potts almost snatched victory for Carlisle with a fierce right-footed drive which went narrowly wide after a barnstorming run through the middle.