The English Football League convened on Wednesday for a further meeting amid the coronavirus crisis, having announced a suspension of its competitions until April 3 at the earliest in response to the global pandemic.
Chairman Rick Parry insisted that "now is the time for cool heads and calm reflection" as he and his organisation refused to be drawn on speculation concerning how or if the 2019-20 season can be completed.
Oakwell CEO Murphy believes that to protect the integrity of the sporting competition, the season must be finished, but believes that there urgently needs to be clarity and a given time-scale for completion.
As it stands, with nine games of the Championship season to go, Barnsley are bottom of the table and seven points adrift of four-from-bottom Hull City.
Murphy said: "In terms of how to move forward as a league, I think in these circumstances all self-interest should be cast aside.
"This is about the greater picture.
"From a sporting perspective, we believe the season should be finished, the games should be played. But that's up to the powers-that-be, such as the EFL and the government.
"But it's our belief that the games should be played. If that's behind closed doors, then so be it but I think that throws up a lot of other questions too.
"Our one caveat would be the timeline. There would have to be an end-date, as to when the fixtures would need to be completed by. We have to have a timeframe for everything, we cannot run in limbo.
"You've to think about player contracts, deadlines around the transfer market, player trading, and of course we have deals in place with our suppliers, what about our seasonal memberships?
"All of this needs clarifying. How do you proceed as a football club, in terms of longevity without any time-frame to work within?"
The financial ramifications of leagues being out of action for a significant length of time have prompted fears, especially in the lower divisions, of grave consequences for clubs, with League One and League Two clubs reportedly asking EFL bosses to address the £50million black hole facing them.
Offering a Barnsley perspective, Murphy confirmed that Barnsley are fairly well placed to cope with a financial hit in the short-term at least, but admits he harbours fears for those down the pyramid.
He did go onto warn that any longer-term shut-down would have far more potentially more far-reaching effects for the club.
"Thankfully, due to the way we operate as a club, in terms of our approach and philosophy, this allows us to be in a stable place to cope from a financial standpoint right now," he said.
"We believe we can take on any waves that may come in the weeks ahead.
"But long-term? Who knows how long this will continue, but I do believe the impact throughout the EFL and its clubs will become greater and that some clubs will struggle financially.
"I think without plans or help in place, there will be clubs in trouble."