Although the initial postponement of fixtures currently takes clubs up to April 30, it is expected a significantly longer delay will be on the cards before league football resumes.
Parry says the 2019/2020 season will be completed but admits it is impossible to estimate what impact it could have on the following campaign.
“We are committed to finish the season on the pitch,” he said. “We want promotion and relegation.
“We don't want an artificial end to the season. When that will be, how that will be, no one knows at the moment.
“There are greater priorities in looking after the nation's health which we must never, ever forget.”
Playing behind closed doors is an option available to the EFL with the government banning large gatherings for the time being as they battle the virus outbreak.
If the season extends beyond the end of June a number of contractual issues will arise, particularly at Wanderers where 15 professional players will become free agents.
But Parry wants all organisations involved to appreciate that patience and understanding will be necessary if a compromise is to be reached.
“People realise there is no rulebook for this, no manual,” he said.
“We're going to have to be incredibly flexible in terms of how the season pans out.
“We don't know whether it's going to be behind closed doors, we don't know when it's going to be recommence.
“We also don't know when next season is going to start.
“The idea that this is going to be neatly over in June and next season starts in August, is wishful thinking.
“I think there's going to be a knock-on effect for 18 months.
“So we'll need a lot of flexibility, outside-the-box thinking, and more than ever, cool heads.”
The financial future of many clubs outside the top flight is also a matter of serious concern.
The EFL advanced prize monies and basic payments last week and will also make available an interest free loan which could head off some of the short-term problems.
But some clubs living close to the bread line have already stated the financial help will not be enough to see them through what is expected to be a long delay without gate receipts.
Parry admits the EFL are not in a position to advance any further funds.
“That'd be a stretch,” he said. “The money we advanced was on the basis that it ought to be enough to get through the next three wages of matchday revenue, which is the first loss.
“What it doesn't do is come anywhere remotely close to covering the wage bill for the period, but we don't have a money tree and nor does anybody else.
“There's no simple answer, but what we've got to be very careful of is kicking the can down the road.
“The more we defer, the more we lend, the more we're going to have a problem in three or four months.
“We need to find long-term solutions as far as we can.”
Parry also said going to the Premier League for financial assistance was not a measure he favoured.
“I'm not a fan of the begging-bowl culture,” he said. “I think it's much better to be in dialogue with the Premier League about sustainable futures and how we might have a reset going forward.”