Brandy, a 63rd-minute replacement for Jamie Murphy, inexplicably steered his 85th-minute effort wide before seeing red for a challenge on Dons defender Lee Hodson.
The defeat stretched their winless run in all competitions to five matches and Weir said: "I think anybody who was here today would solidly agree that we did enough to win the game but ultimately we didn't and it's a big, big disappointment.
"We did so many things right but when the opportunities came we just couldn't finish them off and that, ultimately, is the business we're in.
"When you read the papers tomorrow and we lose 1-0 and you hear the score, it's a disappointment. I realise the facts of the industry but watching the game you realise there were so many positives and we created good chances, we just couldn't get them across the line.
"There's like a pain you feel when you see it happening and it's just really, really disappointing. I think it's just the mentality, I think we've just got to find it within the dressing room, within the group first and foremost.
"Like I said, I think we did enough to win the game and it's almost like a belief in ourselves that we can do that, that we can win and what we're doing is going to be successful.
"Ultimately you're judged on results, though, and today's result was disappointing."
- Sports & Recreation
- Febian Brandy