An early goal from Robin Hulbert was enough to secure all three points for the Quakers.
McParland slammed his side's defending for the goal and was also critical of his players' lack of endeavour after they failed to get back into the game.
"I can't understand what happened out there. We never got going in the game at all and that is what disappoints me most," said the Scot.
"We conceded a sloppy early goal - it was a schoolboy goal to give away, it was a disgrace. It gave us a mountain to climb but then we failed to trouble their keeper for the rest of the game. As a team we have to do a lot better than that.
"We knew we would be in for a difficult game but, to be honest, we didn't cause Darlington any problems. We saw plenty of the ball in the second half but failed to do anything with it."