The Clarets had to battle hard to secure the point that kept them top of the Sky Bet Championship table at the City Ground against a Forest side that pushed them all the way.
Forest dominated for long spells, but needed a goal from Simon Cox three minutes before half-time to cancel out Sam Vokes' 28th-minute penalty for Burnley, who extended their unbeaten run to 12 matches.
"We picked up a point at Nottingham Forest and we are top of the league and it is hard to be disappointed - but I like the fact that there was a little disappointment after this," said Dyche.
"There is no lack of effort, we just lacked a little quality on the ball. We have not had to defend that hard very often, but you expect that here. They have overwhelming resources. Still, they did not manage to break us down too often. This is a tough place to come.
"We have 20-something players who are working hard for the cause. Billy Davies has spoken about his injuries, I think he was down to 32 players today."
Burnley's goal came after Gonzalo Jara had handled Kieran Trippier's cross - and the two managers disagreed over whether the penalty should have been given.
"I am told that if your arm is in an unnatural position and the ball hits it, it is a penalty. If you go by the rules, then it is a penalty," said Dyche.
Davies, on the other hand, said: "With regards to the penalty, I agreed with the linesman, I am sure their manager will agree with the referee. I have seen the incident again and I agree with the linesman (who did not signal for a penalty)."
But the Scotsman was delighted with Forest's performance, adding: "It is a travesty that we did not get three points. There was only one team that was going to win this game.
"I was delighted with the performance. We played against the top of the league side and we had total dominance, nullifying them, barring five minutes. We deserved a lot more than we got. I am very proud of the players.
"I was pleased with the manner in which we went about our business, with the football we played, with the dominance we had. There have been many games where we have deserved more than we have got and this one was another.
"We lost some key players. We lost Eric Lichaj to an injury at half-time and Chris Cohen late in the game. He has a knee problem, in the same knee he has had issues with previously, we will find out how bad it is (on Sunday)."