Bees boss Uwe Rosler admitted he will dip into the transfer market after his side's lethargic showing against the resolute, but unadventurous Cumbrians.
Abbott said: "Our main aim was to get men behind the ball as quickly as possible whenever we lost it and it worked very well.
"I don't think Brentford had a clear chance on goal.
"Make no mistake this is a great point and one we will take a lot of confidence from.
"We worked hard as a team and were great value for the draw."
Abbott admitted surprise at the home side's lacklustre display, but added: "Brentford are a very good side and will be up there at the end of the season - and that makes this point even more priceless.
"We came with a game-plan and on that display Brentford would have been better as the away side."
Brentford looked more lively when they went down to 10 men after centre-back Craig saw red for a professional foul on David Amoo following a heavy touch from Scott Barron.
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 David Button's reflex save.
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.