Bradden Inman's late strike gave Alex the points but Troy Hewitt, Tom Hopper and Steven Schumacher all went close for the visitors.
Blackwell, who cannot add to his squad after the club was this week put under a transfer embargo by the Football League, said: "With the chances we have had I can't believe we haven't won the game, let alone lost it.
"We were fantastic but all the good work we put in was wasted when we let ourselves get mugged in the last minute.
"It is obvious where the problems are. As a manager I have tightened things up and we look a decent side but we need to make changes - but I can't bring anyone in.
"I don't know what the financial situation is and that's the problem. You need to ask the people in charge of the club. They are the wise men and seem to know what's going on. I don't.
"It's frustrating because I know what a good manager I am and what I can do."
- Sports & Recreation
- Tom Hopper
- Steven Schumacher