Jimmy Ryan's 25-yard free-kick put Stanley in front after 26 minutes, but an unmarked Bilel Moshni levelled for the Shrimpers in the 65th minute, heading home Sofiene Zaaboub's set piece.
Accrington played out the last 12 minutes with 10 men after Peter Murphy was given a straight red card for a challenge on Anthony Grant.
"It was never a free-kick for the goal and we are disappointed with the sending off too," said Coleman.
"With the sending off we are convinced that Murphy had the ball. First the referee gave a throw-in, then he gave a free-kick and then he sent him off.
"We are not a dirty team and it was not a dirty game."