Jake Speight put Cox's team ahead in the 75th minute and they looked on course for a win until Kal Naismith converted from the spot.
Cox, whose side were looking for a fifth successive win, said his players were angry as they felt James Gray was offside before he won the late penalty.
"The lads are furious but we shouldn't have been in that position in the first place," said Cox. "It was a strange end to the game as, after we scored, I just felt we would ride it out like we have done in the past.
"But when we scored we seemed to panic and lose our shape. We know Stanley keep going until the end - we saw that at our place earlier in the season when they scored two late goals - but we went to sleep."