The United captain, who was returning to the side following a lengthy lay-off with a calf injury, was handed his marching orders for a high challenge during the second half of United's 2-0 victory over FC Oțelul Galați.
"I wouldn't think so," Ferguson replied when asked by Sky Sports News if he was planning to challenge the decision. "I don't think you win these things."
Ferguson also admitted that he could see why the referee decided to send off his skipper, although he has described the verdict as "very harsh".
"[Vidic] has raised his foot and in the context of referees interpretation in Europe, I can see why he's given," added the boss. "But it was very harsh."
Vidic will now be suspended for the return meeting in two weeks' time.