Romain Vincelot put the Daggers ahead in the 76th minute but the Grecians hit back in style.
Matthew Taylor headed an 81st-minute equaliser and Richard Logan then buried a fine cross from Daniel Nardiello to settle matters.
Still said: "I am disappointed because I think we did enough to win the game.
"At 1-0, I think we had the initiative, but it was two lacks of discipline that have cost us.
"We had plenty of chances before we got the goal and a few scrambles.
"Football being what it is doesn't always work as it should do, but we will go back and work on it again this week."
Source: PA
Source: PA