The closest either side came to breaking the deadlock was when Bees' second-half substitute Toumani Diagouraga fired home from close range only to see the effort ruled out for a foul on goalkeeper Mark Gillespie.
Referee David Phillips was the star of the show with a string of inconsistent decisions and yellow cards as the physical Cumbrians kept 11 men behind the ball.
Brentford huffed and puffed to break down a resolute defence, but their cause was not helped when centre-back Craig was sent off on the hour for a professional foul on David Amoo.
Brentford rarely threatened, but came close just before the break when Clayton Donaldson headed Sam Saunders' far post cross just wide.
Carlisle might have staged a smash-and-grab just after the interval when Lee Miller deflected Matty Robson's free-kick goalwards only to be denied by a reflex save from David Button.
Adam Forshaw's dipping drive was parried to safety by Gillespie and Donaldson's snapshot from the edge of the box was blocked as the home side pressed for the winner.
The Bees thought they had the perfect chance almost on full time when Donaldson appeared to be hauled off the ball in the box, but the referee waved away the protests.