The centre-half's clearance hit a prone Van Persie at point-blank range during United's 1-1 draw in south Wales, prompting an angry response from the Dutchman.
Williams - booked at the time - afterwards insisted it was a complete accident, but a simmering Ferguson claimed Van Persie could have been killed and called the act "absolutely deliberate".
He told Sky Sports: "I think the FA has got to look into it. Irrespective of him having a yellow card he should be banned for a long, long time. It's the most dangerous thing I've seen on a football field for many, many years.
"(It was) absolutely deliberate. the whistle's gone, the game has stopped and he's done that a foot from the player. He could have killed the lad - it's a disgraceful act and he should be banned for a long, long time."
Williams said: "I tried to clear the ball it hit him on the head. I was trying to clear the ball. He was obviously a bit angry about that. It was a much ado about nothing."
Asked about Ferguson's reaction, Williams told the Daily Telegraph: "It's his opinion, he's entitled to it. I understand why Van Persie was angry but I've kicked the ball away in frustration, I wasn't trying to hit him in the head.
"I tried to say sorry but he wasn't having it. I haven't spoken to him since the game and I didn't shake hands afterwards, but only because I didn't see him. As far as I'm concerned, it's no big deal.
"If I had tried to hit him on the head deliberately, I would have missed! It's not like I'm going to shoot and hit him square in the head like that."
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