The centre-half was sent off following an off-the-ball clash with Blades forward Dave Kitson during Tuesday's dramatic 2-2 draw in which team-mate Clayton Donaldson and United's Harry Maguire also saw red.
Bees manager Uwe Rosler was confident the appeal would be successful, saying: "I have seen the DVD. Tony was fouled. Kitson wrestled him down. Tony had his arm up but there was no movement.
"We will definitely appeal and I think we have a good chance, after seeing the footage, that justice will be done."
But the Football Association rejected the appeal and Craig will now be suspended for Brentford's final two matches and the play-off first leg if they are involved.