The Premier League's £50million rescue package for clubs in Leagues One and Two was "wrong on so many levels", according to Portsmouth chief executive Mark Catlin.
The EFL rejected the offer, designed to assist clubs affected by the coronavirus pandemic and made up of grants and interest-free loans, after divisional meetings with its clubs on Thursday.
The EFL said the offer "fell some way short" of what was required, and said any rescue package had to include clubs in the Championship as well.
Catlin said there had been unanimity among League One clubs in rejecting the offer.
He told the PA news agency: "It was far too little, too onerous in regards of the strings attached and didn't offer any real solution moving forward. It was divisive at a time when we needed unity, it was wrong on so many levels.
"It is woefully short of what's required. The EFL has been saying since the beginning that there's a £250m black hole. The offer is embarrassing. I've been very defensive of the Premier League but I lost a lot of respect for them with that offer."
The Premier League is understood to strongly dispute the assertion from the EFL that the offer was conditional, and its position is that clubs just needed to demonstrate hardship as a result of the pandemic in order to secure the support.
Asked what strings he thought were attached, Catlin said: "Things affecting future competitions, things affecting the academies, and in no small part that this was just offered to League One and League Two.
"If you're trying to assist an organisation, you can't cause divisions. The EFL feels very isolated at the moment, we don't feel we're being given any help, from the Premier League and primarily the Government."
The Premier League is understood to be prepared to engage with any club, including those in the Championship, who believe they are under immediate threat. It announced on Wednesday that discussions were continuing with the EFL over support for Championship clubs.
Catlin said the Premier League needed to fulfil the "promise" to help the EFL which the Government has said was a condition of it supporting Project Restart in the summer.
The Premier League's offer came less than a week after details of Project Big Picture plans emerged.
PBP was initially developed by Liverpool and Manchester United and publicly endorsed by EFL chairman Rick Parry, much to the disappointment of the Premier League. Its chief executive Richard Masters spoke on Wednesday about the need to "re-establish trust" with the EFL leadership after the events of last weekend.
The proposals made provision for an immediate £250million package for EFL clubs and a 25 per cent share of future Premier League media revenues, but were criticised because they also sought to concentrate greater power in the hands of the top flight's 'big six' clubs, and were rejected at a Premier League meeting on Wednesday.
Despite the EFL's collective rejection of the Premier League offer, Forest Green chairman Dale Vince said there was a possibility one or more clubs would be in such dire straits that they could break ranks and go direct to the Premier League for help.
He said it was "decent" of the Premier League to leave the offer of support on the table, and added: "There may be some clubs that are in dire need and it may take too long for an alternative to come.
"Somebody may have to go to the Premier League and say, 'look, we're about to not be able to pay wages' or something, but that's not our position.
"We have lost revenue like everyone else has, but we've made adjustments and we can make more adjustments if we have to."
Vince also said his understanding was that the offer was conditional. Asked who set out what the conditions were, he said: "It's what the EFL board said. What I have seen set out is that the Premier League would stay in control of the dispersal of the money, alongside the EFL and it was very much going to be a means-tested thing as I understand it."
Prime Minister Boris Johnson's official spokesman was asked about the Premier League bailout for the EFL at a lobby briefing on Friday.
He said: "I think we have been given assurances by both the Premier League and the EFL that they have no intention to let any club go bust due to Covid.
"And we know that they have the means to prevent this from happening within their existing mechanisms. We strongly urge the Premier League and the EFL to continue to work constructively to come up with a deal that provides a comprehensive package of support for the whole football family."