Smith was sent off deep into injury time in Saturday's fifth-round tie at stadium:mk following a challenge on Rory Delap in which the former Leeds and Manchester United striker led with an arm whilst jumping.
Dons boss Karl Robinson said after the game he felt referee Michael Jones was too quick to pull out the red card and, after seeing a replay of the incident, he hopes to get the decision overturned.
"The referee told me it was for contact in the back of the head. I've seen it back, and his contact was below the arm," said Robinson.
"It's a joke. Rory Delap didn't even think it was a free-kick. It's not a sending off.
"I'll appeal that, I might as well go to another dubious panel."
Smith's dismissal was the third straight red card shown to a Dons player in the last five matches.