Colin Calderwood's men had been dominant in a first half that saw Grant Holt fail to score from the penalty spot and Neil Harris and Wes Morgan both have efforts cleared off the line.
And they were almost made to pay the price as Carlisle's confidence grew after the break with Paul Murray failing to convert a fine Chris Lumsdon cross from point-blank range and Karl Hawley forcing a fine save from Paul Smith.
It was a vast improvement on Forest's performance against Oldham in midweek when they suffered their first defeat of the campaign.
But Calderwood was still left frustrated following what will be seen as another slight hiccup in their promotion push.
Early on Simon Hackney had a great opportunity to put the visitors ahead as he turned in space on the edge of the Forest box, but after showing neat feet initially, his shot lacked menace as it was fired weakly at keeper Smith.
Junior Agogo had looked lively on his first full start for the Reds and almost carved out an opening goal for Forest with a cleverly flighted ball into the box for Harris who planted a downward header that had Keiren Westwood scrambling to palm desperately around the foot of the post.
Grant Holt was also confident and forced a capable save from Westwood in the opening stages as he burst into the box from wide on the right.
But Forest were left wondering how they had not taken the lead after they were denied four times in quick succession.
The first chance saw Morgan thunder a header goalwards from a Nicky Southall corner only for Hackney to clear off the line at the far post.
They came even closer moments later after good work from the lively Agogo who cut into the box from the right with some menace before squaring a neat pass to Harris.
The striker stepped neatly inside his marker before driving a shot towards the far corner of the net which was headed out from under the bar by Kevin Gray.
Grant Holt then had the ball in the back of the net after finishing confidently from the edge of the box only to be left with his head in his hands when the referee spotted an offside flag.
Goalkeeper Westwood was to deny them their best opportunity after Peter Murphy had hauled down Agogo in the box.
Grant Holt stepped up confidently to take the penalty but failed to get much power behind his shot which Westwood pounced on diving low to his left.
Forest were left frustrated again as they had a second goal disallowed, although this time the hand ball from Harris seemed almost as emphatic as his subsequent finish into the roof of the net.
Carlisle again almost caught Forest on the back foot as Lumsdon carved a chance out of nothing as he produced a clever header from just inside the box which looped on to the roof of the bar and out.
Southall hit back with a driven shot that Westwood was again well placed to save at his near post.
But Carlisle grew in confidence again and should have scored as Lumsdon fired a superb ball across the face of goal which Murray somehow failed to touch in at the far post.
By the end although they had half-hearted late penalty claims through substitute Jack Lester and Agogo, it was Forest who were hanging on for a point as Carlisle put them under pressure in the final stages.