In an interview on TalkSport this afternoon, Keys claimed that he was asked not to make public the fact that he had telephoned Sian Massey to apologise on Sunday afternoon.
Keys referred to "a firestorm raging out there" that was "very difficult to step into the middle of" and said that he hoped to "correct the misinformation that's been put about".
"I would like to reiterate what I said to Sian Massey on Sunday afternoon... not as reported after this storm blew up," he said.
"There is no excuse anywhere for anybody to make a judgement on someone's ability to do a job because they are male or female - that was wrong."
Keys added of his conversation with Massey: "She was in good spirits and I expressed my disappointment that Andy and I in misguidedly having a little fun got it wrong... she and I enjoyed some banter together - we left on very good terms."
He continued: "Am I defending what we said or did? No - I've never had a problem saying sorry when I'm wrong. It was wrong, we were wrong.
"On behalf of Andy and myself we unreservedly apologise for our behaviour. [I can] stand up and get battered because I deserve to be."
However, Keys also added that there were "dark forces at work here", noting of his apology to Massey: "I asked could we make public that we had a conversation and could we move on - I was told no. I don't know why I was told no - I don't know why I was stopped.
"All I can do is sit here and apologise for our behaviour. I cannot believe the frenzy that's blown up. If I'd been able to get out the fact that I said sorry on Sunday I think it wouldn't have done.
"I reacted to it immediately when I knew it was a problem. I rang Sian... I rang Karren [Brady]. She refused to accept my call."
Of Brady's response to the storm, Keys noted that the matter had forced the problems at West Ham United - of whom she is vice chairman - from the back pages.
"She knows and everybody else knows what a mess they made of [trying to appoint] Martin O'Neill," he claimed. "She played that card, rightly or wrongly."
Regarding Rio Ferdinand's criticism of the "Lads' mag humour" he had exhibited, Keys said: "Rio, does it not take place in the Manchester United dressing room? My information is it does."
Keys also criticised the front cover of The Sun, which featured Massey out at a nightclub with the headline "Get 'Em Off".
"To put a picture [like that] of her on the page was in my opinion not right - particularly in these circumstances."