Jim Gannon made three changes from the side that won at Carlisle in midweek.
Adam Nowland, cup-tied at Brunton Park, came in for his County debut.
And Jason Taylor returned after serving a one-match ban.
The other change saw Michael Rose make his first start since recovering from his cruciate ligament reconstruction.
Greg Tansey and Paul Turnbull dropped down to the bench with Keith Briggs (ill) not included at all.
County looked hungry from the outset; Griffin in particular was causing some problems on the left flank.
The confidence of Tuesday' result was plain to see as County played some great football.
The first real chance of the game fell to Adam Proudlock when he headed from inside the area, but his effort went over the bar. At the other end Lionel Ainsworth's bursting run created a right wing shot that was caught by Logan.
A good build up from the home side saw Adam Proudlock deliver a delightful ball across goal for the on-running Anthony Elding but there was too much pace on the ball for him to apply a deadly execution.
A good ball from Griffin moments later found the head of Dickinson, who was lurking at the far post. Unluckily for County the ball bounced off the line and was soon cleared by the Hereford defence.
Hereford drew first blood though, when the impressive Lionel Ainsworth scored a wonderful goal from the edge of the area that looped beyond Logan's grasp.
Ainsworth grabbed a second goal minutes into the second half with a far post header from a Trevor Benjamin cross to send the home fans into stunned silence.
Elding pulled one back through a penalty kick after Benjamin pushed Dickinson in the box. After this County peppered the Cheadle End as they went in search of an equaliser, yet unbelievably they were further behind when Ainsworth grabbed a hat-trick with a neat finish past Logan. Guinan nearly made matters worse moments later, but thankfully Logan was equal to his shot.
County grabbed a consolation through a Wayne Brown own goal but it wasn't enough. Despite a much-improved performance, one player made all the difference today. It was just a shame he wasn't playing for the boys in Blue.
