The 6ft 6in forward was a half-time substitute but was sent off inside the first minute of the restart by Lee Probert after colliding with Reda Johnson.
Smith was shown a straight red card and if the appeal is unsuccessful he will serve a three-game ban, starting with next week’s home game against Leicester.
“It wasn’t a sending off,” said McDermott, who revealed he had spoken with Probert about the dismissal.
“There’s no way that’s a sending off. Matt caught him but he was trying to make an honest challenge.
“I didn’t think it was a booking quite frankly and the referee’s got to look at it. They have to rescind it and if they don’t, it’s not right.”