The Manchester United forward was lying on the ground following a foul when Williams kicked the ball into the back of his head during yesterday's Barclays Premier League match at the Liberty Stadium.
United manager Sir Alex Ferguson said Van Persie was "lucky to be alive" after the incident in the 74th minute of the 1-1 draw.
But Liverpool boss Brendan Rodgers, who was Williams' manager at the Liberty Stadium until he left in the summer, felt the issue had been blown out of proportion and was an unintentional mistake by the defender.
"I think more has been made of it than what it actually was," Rodgers said.
"When you slow it down and look at it 20 times it does not look good for Ashley.
"But I know the player well and it is just that split-second when you can see he is trying to clear the ball and unfortunately hits Van Persie right on the back of his head.
"Of course, it looks dangerous but knowing Ashley he won't have meant it, knowing his character that won't have been intentional."