The Shakers went into the half-time break 1-0 up after skipper Stephen Schumacher's terrific strike as County struggled to get going.
However, the hosts were revitalised after the break and scored three times in a seven-minute spell, with substitute Francois Zoko grabbing a brace and Jamal Campbell-Ryce completing the scoring from the spot.
The spotlight was on Blackwell's defence afterwards but a transfer embargo means he is unable to bring in reinforcements.
He said: "That six or seven-minute period (when County scored three goals) we went all over the place. Young Ashley (Eastham) didn't play well and made a mistake but he's 19 years old (Eastham is, in fact, 21) and I said to him, 'If you want to be a pro you're going to make mistakes as a centre-half'.
"Unfortunately he had young Ethan (Ebanks-Landell) beside him at 19 so there was no help for him. We've been embargoed for too long now and we can't bring players in which makes it very difficult. Finances are tight and you end up having to get 19 year olds to do a man's job and we got undone.
"It's tough. I admire the work the director's are doing trying to turn the finances around but it's tough for everyone at the moment."