The full-back sprawled in the box under a injudicious challenge from Sofiane Boufal during the first half of the Cherries' 1-1 home draw with Southampton.
Referee Jon Moss decided it wasn't worth a penalty and proceeded to book Smith for simulation.
The 26-year-old will now miss Saturday's trip to relegation-threatened Crystal Palace because it was his fifth caution of the season.
But Smith claimed the West Yorkshire official had apologised for the decision after the match.
Smith said: "I don’t know why he didn’t give a penalty. Someone said the ref didn’t have a great view so he guessed but the lino was right there.
"I went up to the ref after the game and he apologised to me and said it was a pen. At least he admitted it so fair play to him. But they aren’t going to rescind it because they can’t rescind a yellow card.
"I don’t know why they can’t. It’s a big decision in the game which will affect me going forward. I had got myself back in the team so to miss out next weekend is disappointing. It’s a double whammy."
Smith also brushed off concerns that he could earn a reputation for diving after being cautioned for it on Sunday.
"I’m not too fussed about that," he added.
"People can see I didn’t dive so I’m not too fussed if anyone thinks I’m a diver or not.
"It’s just the fact I’m suspended and it could have helped us in the game."