The Hatters were on top at Victoria Road until the 38th minute when Benson, a former Dagger, was shown a straight red card by referee Darren Sheldrake for a clumsy, high challenge on Ian Gayle.
The striker’s dismissal carries with it a three-match suspension, thus bringing to a premature end his season – unless Luton can get the decision overturned or reach the play-offs.
“We will appeal,” said Still, who is not holding out much hope.
“When Steve McNulty got sent off earlier this season [against York] and their player got sent off as well, they were so far away from sending offs, I thought it was embarrassing. It was right in front of me and neither of them got off [after appeals].
“We’ll appeal but I don’t give ourselves any chance, I really don’t.
“I’m dismayed at some of the things, if I’m being honest, I really am. We can’t do anything about them.”
Meanwhile, adding injury to insult, Nathan Doyle limped off against the Daggers on Tuesday night with a calf injury.
However, Still added: “I don’t think it’s terrible.”