Dyche insisted that Dexter Blackstock committed a foul before he fired Forest ahead in the 59th minute and Billy Sharp's 76th minute strike condemned the Clarets to defeat.
"There was nothing in the game until the first goal and it should not have been allowed," said Dyche. "I've seen the incident again and it was clearly a foul by Dexter Blackstock on Jason Shackell.
"It's impossible to leap that high and get that leverage without using somebody else. If I can see it 70 yards away I don't see how an official can't spot it.
"It changed the whole game because the crowd were then up and there was a bit of belief back in the team.
"Before that we had done pretty well. In fact for the last 25 minutes of the first half we looked the more likely and arguably should have come in 1-0 ahead.
"We have been clinical in our play, but we weren't today and we just didn't manage to grip the game and come up with a response.
"It was a nearly day for us but there were still some good things in our play - and some not so good."