With Carlisle losing at home to Exeter, Hereford needed a point for second place and secured that from an encounter with very much an end-of-season feel about it.
After Accrington had had rather the better of the opening exchanges, Hereford created the best of the half's chances as the interval approached.
Danny Carey-Bertram made some space on the left and delivered a cross which Danny Williams headed powerfully, but straight at Stanley goalkeeper Danny Alcock.
Adam Stansfield then missed his kick completely after Rob Purdie and Mark Robinson set up a shooting chance and Carey-Bertram saw his appeal for a penalty waved away after he seemed to be brought down in the area.
Hereford came out strongly at the start of the second period and twice might have snatched the lead in the half's opening five minutes.
Craig Stanley had a shot blocked on the line by substitute Rory Prendergast and Alcock produced a fine save to keep out Andy Tretton's header from a Purdie corner.
The Bulls continued to press and Alcock saved well again from Carey-Bertram and Williams, but Hereford were unable to break through with three late long-range efforts from substitute Lee Mills sailing wide of the mark.
"It would have been nice to have finished with a win," said Graham Turner. "We had two or three good chances in the second half and perhaps we should have taken one of them.
"But when you look back on it all, it's been a good season and there is still plenty to play for."