Oliver Palmer put the Stags in front at the interval but Darren Carter equalised with a second-half penalty after Darryl Westlake's handball, which resulted in his dismissal.
Wilder felt that the decision to award his side a penalty was justified, and focused on the fact they have moved within two points of safety.
He said: "We can talk about missed chances but we've gifted them a goal. We got done on one long ball and we should've dealt with that because that's all they're about and that's all they did all day.
"Our quality around the final third was missing a little bit and we are disappointed with that. When we get into those areas we have to stay calm and get the message into the players that they have to be patient and play.
"I can't see why they have any argument with the decision, the lad handballed it on the line just as we were about to score.
"We know we have to play more than we did today; sometimes we moved the ball quickly and we got into good areas and then there were other times when we took too many touches.
"This was a good chance for us to get a really good result today but with the other results we are a point nearer."