For Stanley, it was their first goalless draw in 104 matches, ironically since a visit to Edgar Street for the final game of the 2005-06 season.
Neither side really looked like breaking the deadlock and the two goalkeepers had little to do as the shooting, which was largely restricted to long range, was mostly off target.
Hereford shaded the early play and Richard Rose, who limped off injured before the end of the first half, might have done better when he surged through a gap in the Stanley defence only to shoot weakly.
Four minutes later, The Bulls had an even better chance when Ben Smith's excellent pass sent Theo Robinson racing through. The teenager sprinted into the penalty area but then shot wide across goal.
Robinson might have also done better in the 22nd minute when he got clear on the right but failed to pick out a team mate, all of whom were massed at the far post.
Accrington however were never out of the action, although they were restricted mostly to long range shooting with Roscoe D'Sane powering a couple of efforts off target.
Robinson caused more trouble for Stanley at the start of the second half after good work with Chris Taylor and then substitute Steve Guinan, but again he failed to hit the target.
Accrington were no better in the second forty-five with Jay Harris and Leighton McGivern blazing wide from distance.
Robinson continued to look the most likely to make the break through but fortune was not with the young striker as he crashed another couple of shots wide from promising positions as the clock ran down.