The Daggers led with 10 minutes remaining courtesy of Luke Wilkinson's header just after the hour mark.
But Stewart Drummond equalised in the 81st minute and the Shrimps netted all three points shortly afterwards when substitute Ryan Williams scored a superb individual goal.
Still said: "It was a poor game I have to admit and it never really got going - even after we took the lead.
"If I'm being honest, I didn't think we played well enough to win the game but I am obviously disappointed that we didn't get a point after going into the last 10 minutes in the lead.
"We didn't produce enough opportunities to get a second goal and when you do that you are always vulnerable and that is what happened in the end.
"We will have to take it on the chin and work hard in the week because we have another important game against Plymouth next week that we have to prepare for."