Tijjani Reijnders had City ahead before Omari Hutchinson struck an equaliser for Forest. However, Rayan Cherki then found a late winner for the visitors.
Dyche said, "The players were fantastic today. Unfortunately the officials had a big part in the game today, we don't want that. Scratching (my head) today looking back at some of the incidents. I just can't believe what I'm watching.
"It's pointless (speaking to the officials). We've done it many times as managers and you get in trouble for no reason. Everyone can see it. There's plenty of people here, TV cameras here. Everyone can see their performance today.
"It was miles off, unacceptable in my opinion, because it effects the game massively. Their centre-half boots the ball away then jumps on the floor as if he's injured - nothing wrong with him.
"The second goal (Morgan) Gibbs-White is clear as day pushed to the floor, nothing given. Then the same player tries to get up and block it and it goes through his body because he can't get in position.
"For me that's an unacceptable performance. Sometimes in life the officials have to come out, the powers that be, and say that they were miles off."