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.”
Stoke could face a battle to keep Xherdan Shaqiri as reports have claimed Mark Hughes wants him at Southampton next season.
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.