Jack Hobbs' first Forest goal gave the Reds a first win in five matches against the Rams - and the Brian Clough Trophy.
The centre-half, signed on loan from Hull City over the summer, headed home four minutes before half-time to preserve Forest's unbeaten record at the City Ground and inflict a first away defeat of the Sky Bet Championship season on Clough's side.
Derby, who had captain Richard Keogh sent off for the challenge on Chris Cohen that resulted in the spot-kick, created very little in way of scoring opportunities but Clough was more than satisfied with his team's overall display.
"I am very pleased with the performance, I thought we were very good," said the Rams boss.
"Once we got the first five or 10 minutes out of the way where they came at us, I thought we settled down and played some very good football.
"We are pleased with a lot of things we did, just not the result.
"Just like at Leicester in the (Capital One) cup in midweek we caused our own downfall again with the goal. We should have cleared the ball first of all and then we lost the man from the corner.
"It is a small mistake but we didn't get away with it and it has cost us the game. Sometimes you get away with things like that but at the moment, with the run we are on, we aren't.
"It is naivety again, we have a lot of young players. We are not getting away with the mistakes we are making and a lot in the opposition penalty area is not going our way either - and we are certainly not getting a lot of breaks from the officials."
Keogh became the fifth player in the last six meetings to be sent off in this fixture when he brought down Cohen 12 minutes from time.
A surging midfield run from Cohen was halted by Keogh's challenge from behind. Referee Simon Hooper pointed to the penalty spot and showed the Rams skipper a second yellow card - but Henderson's spot-kick was superbly tipped round the post by Grant diving down to his right.
On the incident, Clough said: "I didn't think it was a penalty.
"I have seen it back a few times now and it was one of those where the forward has put himself in between the ball and the defender and then the referee has compounded the mistake by sending him off, which we could not believe.
"We have been looking for a centre-half and he is only missing one game but we might have to step it (the search) up now.
"If we can get someone in that is better than what we already have then we will."
Clough was linked with Manchester United centre-back Michael Keane this week and went on to confirm that he is one of around a dozen players that Derby, who are also in the market for a right-sided midfielder, have enquired about this week.
Forest boss Billy Davies used the post-match press conference to take a swipe at some of the criticism he feels the club has taken this season, before praising his players for winning "an important three points."
"It is a good win for us and I am obviously very pleased," said the fiery Scot. "I have to say, it was against a side that, they tell me, are making very good progress - and this one is a shambles.
"I am absolutely pleased about what we are doing so far and now we move on to the next one.
"We were disappointed before the game to have lost (Kelvin) Wilson, (Jamie) Paterson and (Nathaniel) Chalobah. That was a big blow for us.
"And we were even more disappointed to have lost (Guy) Moussi during the first half, that was a big blow for us also.
"We should have scored more goals, because we missed a penalty as well. But, overall, it was a very important three points.
"It was tremendous for the fans to get the bragging rights back because they have not had those for a number of games."