Coventry City chief executive Dave Boddy says his club cannot benefit from a £200m rescue package agreed with the Premier League for Championship clubs.
The interest-free loan is part of an overall £250m EFL package, by which League One and League Two clubs will share a non-repayable £50m grant.
But Boddy says the loan to Championship clubs must be used to cover any PAYE debt - and Coventry do not have any.
"As clubs we haven't really been consulted on it," he said.
"It doesn't do a lot for Coventry City. It's not even a loan from the Premier League. They're covering the interest. The EFL has to source the loan," he told BBC Radio 5 Live.
"The problem we have with it as a club is that we can only use it to pay PAYE [income tax and national insurance] debt and we haven't got any.
"With no match day income for nearly 12 months we have a need for cash for the business.
"We were expecting a no-strings-attached loan. That is what the government's Sport Winter Survival Package is.
"The government has supported 11 other sports in the winter survival package and it hasn't supported football. It should have supported football. We're the national game. All this does is help those clubs that are probably very near to administration."
When the package was announced on Thursday, EFL chairman Rick Parry said it was a "welcome, tangible commitment to the professional game at a time when it has needed it most".
Under the terms of the agreement, loans to Championship clubs will be capped at £8.33m per club and must be repaid by June 2024.
'It won't be enough to ensure survival of all the clubs'
In League One, clubs will receive a minimum payment of £375,000, while League Two clubs will get at least £250,000.
But Dave Bottomley, chief executive of League One club Rochdale, warned "it won't be enough to ensure the survival of all the clubs" in the third and fourth tiers of English football.
"It's a great thing to have and, while not appearing to be ungrateful, for a club like Rochdale, it's probably less than two months of our regular outgoings," he told BBC Sport.
As a side based in an area of tier three government restrictions, Rochdale are further hampered by the doors to Spotland remaining closed to the public as the nation continues to respond to the coronavirus pandemic.
In League Two, Grimsby Town chairman Philip Day was also unhappy at the lack of consultation during this process.
"We're not at all happy," Day told BBC Radio Humberside. "This is a done deal as far as clubs are concerned. Clubs were not consulted whether they agreed or not.
"It's probably one of the biggest decisions the EFL have had to make over many years and they've given the clubs a fait accompli.
"They had a meeting at 24 hours notice on Project Big Picture a few weeks ago. Why on earth could they not also have done that before they did this?
"The grant is split into two. A £30m grant for lost revenue and a £20m monitored grant on the basis of need for clubs.
"That means the clubs that were well run before lockdown probably won't have a need and won't get a share of that £20m. Those that weren't so well run may be able to establish a need and get part of that £20m.
"We were told from day one that any compensation from the Premier League would be based on lost gate revenue, so why on earth have they not already been calculating that. They have the information."
Accrington grateful for 'free money gift'
However, the rescue package has been welcomed by other clubs, with Mansfield Town chief executive David Sharpe saying that the grant was "gratefully received".
"It will go a long way," Sharpe told BBC Radio Nottingham. "It's still a difficult time but it is very much appreciated. I've spoken to a number of clubs and they feel the same, it's great the Premier League have helped League One and League Two out.
"Normally we would do £500,000 plus in season ticket sales and another £500,000 on match-day sales and hospitality, and the additional spend that comes with that. We are down but £250,000 is a big help.
"We probably won't apply for a monitored grant because of the strings attached - it would limit what you can do in transfer windows, the wages you can spend and we wouldn't be running the football club how we'd want to."
Forest Green Rovers owner Dale Vince described the actions of the Premier League in supporting the EFL as "brilliant".
"It's a stand out, unique example," Vince said on Twitter. "The government thought that the Premier League should bail out football, while the country has bailed out rugby, horse racing, the arts, pubs, all sorts of sectors, but does nothing for football."
Accrington Stanley owner Andy Holt added: "The long-term viability of football's distribution model was and still is a major problem.
"But £375,000 minimum for our club is greatly appreciated at a time when the club is stressed. It isn't about quantum or 'is it enough' for who knows what the future holds.
"It is a free money gift from club owners in the Premier League to our club for which we are very grateful."