Current FA chairman Greg Clarke and chief executive Martin Glenn met with Allardyce at Wembley and left the 61-year-old in no doubt he had reached the end of a short road with the national side.

And Bernstein told BBC Radio 5 Live: "The hubris of it all is extraordinary. This is a man earning £3m a year.

"I wonder whether there's a pay-off or not - I hope not, because I don't think 50 or 60 days' work merits a pay-off."

Allardyce was also filmed making indiscreet comments about his predecessor Roy Hodgson, FA president Prince William and his brother Prince Harry, including mocking Hodgson's speech impediment.

"We use the word 'respect' in football a lot," said Bernstein. "This is incredibly disrespectful to Princes William and Harry, it was very disrespectful to a man I've got a great deal of respect for, Roy Hodgson.

"I've got, frankly, very little sympathy."

Former FA executive David Davies said it was "inevitable" that Allardyce had to leave the top job after his comments were made public.

Speaking on BBC Breakfast, Davies said: "I was talking to former players yesterday morning ... and they said they thought it was inevitable, because it would have dogged him from now on in any England career.

"My instinct is certainly he will blame himself. If you have quite openly wanted a job for most of your professional life, you get it and you lose it after 67 days you would be distraught.

"You could argue: was Sam entrapped? But it is the reality and football is not going to change that reality. That is the reality of the society that we live in."

Gareth Southgate will take over on an interim basis for England's next four games but Davies and former FA chairman Greg Dyke both made the case for Arsenal manager Arsene Wenger as a long-term successor.

"Let's look Arsene in the eye and say: 'Do you want to be the manager of England?'" said Davies.

Dyke added: "I'm a great fan of Arsene Wenger, I think he's done a great job over 20 years. If he were to leave Arsenal and the FA can get hold of him, I think he'd be a brilliant appointment."

Glenn said after Allardyce's sacking on Tuesday evening that the decision was made to preserve the FA's integrity as "guardians of the game".

"His behaviour has been inappropriate and, frankly, not what is expected of an England manager," he told FATV.

"We have to stand up for the right behaviours across the whole game. We're the guardians of the game, we set the rules. We have to be seen to apply those rules consistently and evenly."

A pair of former England captains, Alan Shearer and Rio Ferdinand, suggested English football had become a subject of mockery in the football world.

Shearer told BBC Radio 5 Live: "I didn't think England could stoop any lower from what happened in the summer in the Euros (losing) to Iceland. And now, here we are. We're a laughing stock of world football.

"We've got a problem. It's greed, isn't it? We have to be able to accept people laughing at us."

Ferdinand added on BT Sport: ''I think the rest of the football community around the world will just be laughing at us."