"We didn't apply enough pressure in the second half to keep Carlisle penned down and our set plays were ineffective," said Reds boss Colin Calderwood.
"We were 15 seconds away from a fairly satisfactory first-half performance."
Carlisle manager Neil McDonald commented: "That performance was brilliant. It was a huge team performance and I won't single out individuals.
"We didn't give the opposition a sniff in front of goal. Forest are a huge club and this was a fantastic result for us."