Bell was sent off during the 2nd half for what looked like a two footed lunge, however he didn't make contact with his opponent.
"I am gobsmacked the appeal has been turned down and for Belly to get an extra match ban is a disgrace," Boss Billy Dearden told the Nottingham Evening Post on Wednesday.
"If it had been a bigger club then we might have been ok, but I think they are hammering the smaller clubs.
"The FA committee had to decide if it was a frivolous appeal and decided it was, which I can't understand at all.
"Because of that they he has to miss another game and I think that's diabolical.
"The trouble is there is no way we can appeal against the decision like you can in the law courts.
"I saw a lad go straight down (Caleb) Folan's shin on the television last night and he didn't even get a yellow card.
"Belly's was not a nasty tackle or a late one, so I'm very disappointed by what's happened."