The Scotland international was dismissed for a studs-up challenge on Wayne Rooney at a snowy bet365 Stadium, leaving his side down to 10 men for an hour of the contest.
Adam concedes that the dismissal, which came with the score still locked at 0-0, cost his side a chance to take all three points from what was labelled a must-win game prior to kickoff.
"I've let the team down and I've let the squad down," he is quoted as saying by The Mirror. "I was surprised it was a red card. I thought he was going to pull out yellow. The conditions weren't great and Wayne's got there before me. You've got to take the conditions into account but he is happy with the decision he's made.
"I went to see Wayne to see if he thought it was a bad tackle. He said, 'Not really'. I've been in to see the referee and he's still happy with his decision. It's part and parcel of being a footballer isn't it? You have ups and you have downs. When you're down, you're down."
Stoke, who welcomed a record crowd of over 30,000 to the bet365 Stadium, are three points from safety with seven games left to play.