The club made an appeal for £1m of funding last week, in a bid to preserve their future.
Blackwell, who was appointed manager in September, has said that he considered his position after the first of two transfer embargoes were imposed over the Gigg Lane club in 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 told the Manchester Evening News.
"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."
Bury were relegated to League Two following their 1-0 defeat to Oldham Athletic last Saturday.