The Ashes great, 47, had been accused by former team-mates Rafiq, Adil Rashid and Rana Navedul-Hasan of saying “too many of you lot, we need to do something about it” ahead of a county match in 2009.
In his first TV interview in the wake of the racism allegations, Vaughan repeated that he had “no recollection” of the incident and claimed he was as “proud as punch” about having four Asian players representing the club.
The fourth player, Ajmal Shahzad, has said he did not hear the alleged comment.
Vaughan, who led the England side that won the Ashes for the first time in 18 years in 2005, told the BBC: “I don’t [remember the incident]. My recollection from that day, as I’ve said, I was a Yorkshire player for 18 years, I was the first player to sign for that club that was not born in the county.
“So for 18 years we have gone from me being the first to sign for the club, Sachin Tendulkar being the first from overseas, to players being able to sign from other clubs.
“It was my last few games and I remember it clearly that I was proud as punch that we had four Asian players representing Yorkshire County Cricket Club.
“Yorkshire County Cricket Club, in particular, has not dealt with this situation at all well. I see a young lad [Rafiq], someone that I played with that has gone through a huge amount of hurt. I have to take some responsibility for that as I played for Yorkshire for 18 years and if in any way, shape or form I am responsible for any of his hurt, I apologise for that.”
Vaughan was stood down by the BBC from their Ashes coverage this winter after allegedly making the comment ahead of the 2009 T20 match between Yorkshire and Nottinghamshire.
Footage shows Vaughan shaking hands with the four Yorkshire team-mates – Rashid, Rafiq, Navedul-Hasan and Shahzad, with them all laughing.
Rafiq claimed that Vaughan said: “There are too many of you lot. We need to do something about it.”
Rashid and Naved-ul-Hasan said they backed the claim but former seamer Shahzad said he did not hear the exchange.
Of the allegation Azeem Rafiq to MPs made against him,Vaughan added: “That hurts, because I’ve always felt that every single team that I have been involved in, the biggest praise I ever got as England captain for six years was that I was the kind of person that really galvanised the group, got the team working together as one.
“I wanted everyone in the dressing room to feel included.”
And on Rafiq, the former England skipper said: “I’m sorry for the hurt that he has gone through.
“Time can never be a healer but, hopefully, time can be a way of Yorkshire Cricket Club never going through this situation again and not putting themselves in a position of denial that they treated the players so badly.”