Phil Edwards put Stanley ahead from the penalty spot after Tom Adeyemi had handballed but on-loan Jason Price claimed a leveller after a scramble in the penalty area.
Coleman said: "I am disappointed that two points were thrown away. I am devastated we have not won.
"We were miles better than Bradford in the first half but they were given a lift with their goal. Our boys are blazing in there. They thought it was a foul on our goalkeeper. If it wasn't a foul on Ian Dunbavin then it was dangerous play.
"It is hard to take. You feel it is all for nothing."