Talks with the PFA over a collective approach for all Premier League clubs broke down last week, leaving individual clubs to take things forward.
But Bloom warned that focusing on defending players' income in the short term could endanger jobs and clubs as the shutdown continues.
"It is time for the PFA to step up to the mark, to really look at the situation around the long-term implications of not being more open to some of the suggestions," Bloom said speaking on conference call.
"Particularly lower down the leagues, some of these clubs are going to be under huge financial pressure - are under huge financial pressure - because of player salaries.
"And it's thinking about when those existing players' contracts run out. Is it in their interests if the PFA are too intransigent?
"And for the younger players who don't even have contracts, for the long-term good of the game, I just think, in this particular situation, they really do need to be more open-minded to such a difficult situation for the football club.
"The last thing we need as a football industry is so many clubs to go not only into administration but perhaps not even getting out of it.
"There is a wider picture here and the PFA has a wider responsibility."
Brighton remain in talks with Lewis Dunk and Glenn Murray, who are working on behalf of the entire squad, about the steps they may take.
Bloom warned the shutdown put the future of several clubs at risk, and said it should lead to a wider review of football's sustainability given several clubs spend significantly more than half of revenues on player wages.
"After this situation has resolved - hopefully that doesn't take too long - I do think football will come together," Bloom said. "Because, at the moment, a lot of our football clubs are at risk of not only going into administration but going bust.
"We were all devastated when Bury went out of existence. We know how key these football clubs are to their community. So, it is a big concern going forward that more clubs in this country and other countries will fold.
"I think it does need to be looked at, at all levels, as it really is unsustainable and I think it needs something like this crisis to perhaps get across some significant, sustainable change."
Asked if that change could come in the form of a salary cap, Bloom warned it would be very difficult to implement as it would only be effective if it covered leagues across Europe or further beyond.
"If it's going to work, it needs to be worldwide - certainly Europe-wide - and I see big difficulties with that," he said.
"But if it is workable and if leagues, at least around Europe, if not the world, can come to some agreement on it - and I'm sure there are some legal issues there as well - that something, I think, does need to change.
"Otherwise, salaries, player salaries, will always increase far too much and it becomes unaffordable for clubs."
Premier League clubs are due to meet on Friday to discuss the next steps, with reports emerging that a growing number are calling for the season to be ended - one way or another - no later than June 30.
"We would like to finish the season," Bloom said. "There does come a point when we can't keep waiting but I don't think June 30 is that point.
"There's talk about player contracts and sponsorship and it's difficult to play beyond that but this situation is so unique and unprecedented every option should be looked at."
While there may need to be short-term solutions such as rolling contracts for players whose deals expire in June, or complications with the start and finish dates of sponsorship deals, Barber said it was important to keep an open mind.
"What we're dealing with now has broken all the rules in every industry," he said. "It can't be perfect. We're all resigned to the fact it won't be perfect but it's a case of making it as good as it can be."
Those solutions seem highly likely to include playing games behind closed doors for an extended period.
"If we have to play behind closed doors we have to accept we won't have the same product. But equally we have to be prepared it might go on for sometime.
"Crowds probably won't be allowed to assemble in our grounds for quite a while.
"People would love to be able to see a live football match, even if it was behind closed doors, it would be something to look forward to but at the moment we've got to look to every eventuality and manage it the best we can."
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