A hard-fought and scrappy affair saw Marcus Tudgay sent off late on for the Reds but Steve Cotterill's side looked to have done enough to earn a crucial point in their battle against relegation.
Substitute Buxton however netted in the 94th minute of the game to delight the majority of the 33,000 crowd.
So near but yet so far for Forest who edge a point closer to the relegation zone following Doncaster's home draw against Reading.
Cotterill disagreed with the decision to award a free-kick prior to Derby's winning goal but admitted his side were not at their best.
"We deserved a point tonight, no more than that let's be honest," he said.
"But when it's our fourth game in 10 days, we haven't got the ability and the squad to flip players and not to be able to put out our strongest XI.
"So for the effort they've put in, the lads over the last 10 days it's been phenomenal."