Forest came from a goal down to take a 2-1 lead before Amad Diallo struck late for United to settle the score.
Dyche said, “The performance was a marked improvement on the Bournemouth performance. The reaction was first class.
“We came in at half-time a little bit aggrieved, but we didn’t deal with the situation either, which we need to do better at.
“But in the second half, the reaction was excellent. We spoke about that freedom to go and attack the game and they did. We went a little bit deeper as the half went on, but I think that’s to be expected.
“Unfortunately, we didn’t win, but we defended pretty diligently all game, I thought.
“There’s been noise about scoring goals and scoring goals from open play. We’re trying to correct that and we put out a side with the quality to do so.
“It was a great finish from Morgan (Gibbs-White) and a really good finish from Sav (Nicolò Savona). I’m pleased for the players and the supporters in a way, but of course we’re disappointed not to win the game.
“The reaction from the players was absolutely first class, the fans were brilliant. When we got the second, the noise was tremendous.
“We’re going to need that because we have a lot of games coming and a lot of work to do.”