Ross Wallace's penalty cancelled out Curtis Davies' opener for Birmingham, but Marney's dismissal for a dangerous tackle forced Burnley on the back foot and Marlon King snatched a last-gasp winner for the Blues.
Dyche was still satisfied with his side's display, but he feels that referees are too quick to dish out red cards for tackles.
"Some of the football was excellent but you are having to earn wins not just by beating 11, we've having to go beyond that, he said.
"The officials should be there to manage the game and not make decisions that change it radically.
"Apparently [Marney's red card] was for excessive force so I think you've got to tackle softly now.
"I don't think you're allowed to tackle the ball. Maybe you are not allowed to use your feet in a tackle
"You cannot take a great tackle out of the game because it will kill football. All managers want to play the beautiful game, you all want to be a version of Barcelona, Manchester United, Chelsea. But you can't take away tackling. It's what fans buzz off.
"We didn't deserve to lose the game. In the first half we were just off it slightly but then second half I thought we were terrific."