The Yorkshireman made the remarks at a conference in Qatar on Wednesday - comments which the Premier League and Football Association moved quickly to distance themselves from - and later capped a forgettable day by falling into a water feature at an evening function.
He issued a statement apologising on Wednesday night, and followed that up on Thursday morning with more contrition, although he also tried to blame his background for his outspoken tendencies.
He told Sky Sports News: "I'd like to clarify something - I am a Yorkshireman and I am quite broad and if I say something it can be taken out of a little bit of context.
"I was asked about the heritage of the game, I would never want to offend FIFA or UEFA.
"I used a word which was, looking back, probably inappropriate but it is the way I am.
"I put out a statement last night [Wednesday] and I have sent a private email to the president of FIFA and the president of UEFA saying I apologise because I never intended to cause any stir at all.
"I have also phoned (FIFA general secretary) Jerome Valcke this morning and apologised to the president because it wasn't the kind of comment to cause any problem at all.
"What I was talking about is the heritage of the game, that England has given the legacy to the world.
"We were talking about heritage and legacy and England has given a wonderful legacy to the total world.
"It gave them the game and I am tremendously proud of that but I also recognise that UEFA and FIFA have done a magnificent job over the years in changing things and it has got to be changed and I recognise that.
"I just want to say I apologise, it was a comment that probably another person would not have made but I am a little bit broad and I accept that."
Richards' embarrassment heightened following the fall in which he hurt a leg. He had it looked at before being released from hospital.
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."