The Shakers had their relegation confirmed by a 1-0 defeat to Oldham last Saturday - a result that came at the end of a week where the club's board made a public appeal for £1million of external funding to preserve their future.
Blackwell was appointed manager at the end of September and told the Manchester Evening News he considered his future in the strongest terms when the first of two transfer embargoes were imposed at Gigg Lane in early December.
"After the Preston (Johnstone's Paint Trophy) game was called off they pulled me in and told me about the state of play with regards to finances," he said.
"That was on the Tuesday and on the Thursday we went into the embargo which came completely out of the blue. I was angry and they know that.
"It would have been nice to have known that six weeks earlier. I'll be honest, I wouldn't have taken the job.
"I offered my resignation - if they felt that was the right option then I would go and save my wages.
"The board were adamant that I should stay. I talked to a couple of good people in the game and they felt that this was one to stick and fight out."