The Cherries extended their stay at the top of the League Two table thanks to a Danny Hollands header after 76 minutes. The Stanley boss was sent off in the seventh minute after protesting when Michael Symes was booked for a foul on Warren Cummings and Coleman blasted referee Michael Oliver's performance.
Apart from his own dismissal, Coleman was also livid that Stanley were denied a second-half penalty when Anton Robinson felled Andrew Procter.
"Now I can understand why people lose faith in the integrity and ability of match officials. I got annoyed when our player was booked for a foul on their lad - if he did catch him it was marginal," said Coleman. "If a Premiership manager got as annoyed as I did, would he have been sent off? I think not. I think the referee was being a bit petty.
"You cannot legislate for having a stonewall penalty turned down and I think everyone in the ground could see the one on Andrew Procter. It was embarrassing and you'd have to question whether or not the referee wanted to give it.
"We should have got something from the match and I certainly don't think the best team won the game. Unfortunately we lost concentration at a set-piece and they scored. You don't always get what you deserve in this game."