Even if they had forced all three points it would not have been enough to earn them a top-six spot with rivals Swansea and Barnsley both avoiding defeat.
Cheered on by 6,000 noisy travelling supporters, Forest gave it their best shot but were denied by some brilliant goalkeeping from Donovan Ricketts in the City goal.
But it was the Bantams who had started the better side and leading scorer Dean Windass nearly put them in front after just seven minutes when he fired over after exchanging neat passes with Danny Cadamarteri.
Grant Holt then forced Ricketts into a sharp stop before Windass made up for his earlier miss.
Marc Bridge-Wilkinson's 25-yard drive was too hot for Paul Gerrard to hold and City's leading scorer was on hand to tap in.
Forest almost hit back 10 minutes later before Ricketts produced another fine to stop to deny Kris Commons and then made a sharp goalline block just before break.
Forest came out in the second half with all guns blazing and threw everything at City but could not find away past Ricketts until the closing minutes.
Before that the Jamaican international had denied Commons again before producing the save of the match.
Grant Holt had out muscled David Wetherall and fired a shot on target from eight yards out but Ricketts flung himself to his right and palmed the ball wide.
Eventually Forest's pressure did pay off when Julian Bennett bundled the ball in from a corner, but with just two minutes to go it was too little too late.
Both these sides have enjoyed good end of season runs but will be hoping that they can sustain that throughout next season to force their way into the Championship.