"Art imitates life," he said. "I look like the crazy father just like they said about Richard Williams. But love will make you do crazy things."
On Tuesday, Smith unreservedly apologised for the slap, acknowledging his behaviour was "unacceptable and inexcusable".
"I would like to apologise to the Williams Family and my King Richard Family," he said.
"I deeply regret that my behaviour has stained what has been an otherwise gorgeous journey for all of us."
"We don't know all the details of what happened," Richard Williams said, via his son Chavoita LeSane, to NBC News.
"But we don't condone anyone hitting anyone else unless it's in self-defence."
But many were angry the gloss was taken off what should have been a celebration of the Williams family and the careers of tennis' most famous siblings.
Tennis reporter Ben Rothenberg tweeted:"I just feel awful, foremost, for the Williams family, who put so much into making this movie the best it could be, and didn't do anything to deserve how this night imploded."
Former NFL star and Fox Sports host Shannon Sharpe was absolutely furious Smith didn't keep his cool and overshadowed the success of King Richard.
"Now you take the moment away from Venus and Serena, their dad, the story about their family," Sharpe said on his talk show Undisputed.
"You stole that moment from them. Why? Because he (Rock) made a joke?
"For him to do that, considering some of the things she had said at her round table about an entanglement — he ain't slapped that guy! That's the guy you should be mad about!"
New York Times tennis writer Christopher Clarey wrote:"The table was set for a moment of family triumph but then — as so often with the Williamses and through no fault of their own — things got complicated.
"An evening that should have affirmed their against-great-odds rise to stardom instead became about Smith slapping the comedian Chris Rock onstage.
"Sunday night would have been a time to revel in the length of their journey, the depth of their achievements and Richard's legacy. Instead, it turned into a night for Serena to cover her eyes."
For her part, Serena Williams was aghast at the sight of Smith slapping Rock.
A clip she shared on social media featured several seconds of the tennis legend at the awards ceremony in stunned silence, mouth open, not saying anything. In the second video, she said: "I just sat down, because I was like, I gotta put that drink down."