Richards suffered an unfortunate day at a conference in Qatar on Wednesday starting when some controversial remarks caused consternation - and ending when he fell face first into a pool.
Richards claimed this morning that FIFA and UEFA had "stolen" football from England - comments which the Premier League moved quickly to distance themselves from.
The sale of alcohol is severely restricted in the Middle Eastern country and Richards said that needed to be relaxed.
Speaking at the International Sport Security Conference in Doha, Richards said: "In our country and in Germany, we have a culture. We call it, 'We would like to go for a pint', and that pint is a pint of beer.
"It is our culture as much as your culture [in Qatar] is not drinking. There has to be a happy medium.
"If you don't do something about it, you are starting to bury your head in the sand a little bit because it needs addressing.
"You might be better off saying don't come. But a World Cup without England, Germany, the Dutch, Danes and Scandinavians. It's unthinkable."
Hassan Al Thawadi, general secretary of Qatar 2022, has always insisted that alcohol will be available for visiting fans at special zones but he said on Wednesday he did not see the need for beer to be sold in stadiums.
He said: "For me personally, I don't see the reason for it being in the stadiums, but it's something we're discussing with FIFA."
Richards, an FA board member, also launched an attack on FIFA and UEFA for "stealing the game" from England - and over the failed 2018 World Cup bid.
He told the conference that England had given the world the game of football. Richards said: "For 50 years, we owned the game, we were the governance of the game. We wrote the rules and designed the pitches.
"Then, 50 years later, some guy came along and said you're liars and they actually stole it. It was called FIFA. Fifty years later, another gang came along called UEFA and stole a bit more."
He also said FIFA were responsible for England 2018 spending millions of pounds - he referred to £19 million although FA accounts last year revealed the full cost was £21 million - on a bid with the odds stacked against them by FIFA who wanted to take the World Cup to new territories.
He said: "Why couldn't FIFA have said, we want to take it to the Gulf, to the eastern bloc? We spent £19 million on that bid.
"When we went for it everybody believed we had a chance. But as we went through it a pattern emerged that suggested maybe we didn't."
The Premier League have been privately embarrassed by the remarks and issued a statement saying: "Sir Dave is attending the conference in a private and personal capacity and his comments in no way reflect the views of the Premier League."
"The FA greatly values its relationships with FIFA and UEFA, which it is working hard to strengthen."
Richards apologised later on Wednesday for any offence by the remarks which he had intended to be "lighthearted" and said he would be writing to UEFA and FIFA to make that clear.
Richards said in a statement: "Further to the comments I made earlier today at a conference in Doha I would like to apologise for any offence caused.
"It is important to clarify that I was expressing my personal views and not those of any organisation I represent.
"My comments on the heritage of the game were intended to be light-hearted. They clearly have not come across in that way and I sincerely regret making them and any resulting negativity that may have been interpreted towards FIFA and UEFA. I will be writing to both organisations in these terms."
Richards hurt his leg in his fall and had it checked out in a Doha hospital before being released.
Bolton chairman Phil Gartside, who was with Richards at the time, told BBC Sport: "I was on the way to dinner with Sir Dave at the Museum of Islamic Art in Doha. We were walking across to our table in a dark courtyard area. There were three fountain areas nearby, no pool.
"They had switched off the lights. He thought he was stepping on to flat marble, but his foot went down into the water, he fell over and hurt his leg quite badly. Any suggestions he had a drink is nonsense. It's a dry place."