Alan Shifman told reporters outside the family home in the Woodland Hills neighborhood of Los Angeles, reading from a prepared statement on behalf of the family.
"We are experiencing the most inconceivable pain and our hearts go out to everyone involved," he added.
The YouTube video police were studying shows a young man who identified himself as Elliot Rodger pouring out his hatred of women who have rejected him and "popular kids," and threatening to kill people out of loneliness and sexual frustration.
"You girls have never been attracted to me. I don't know why you girls aren't attracted to me. But I will punish you all for it. It's an injustice, a crime," he said in the video, his speech punctuated by bursts of laughter.
The clip, since removed from YouTube as a violation of its policies, appeared to have been uploaded to YouTube on Friday night, shortly before the shooting. Brown said Rodger had also penned a 141-page manifesto, in addition to posting several disturbing videos.
Rodger's killing spree appeared to begin in his apartment in Isla Vista, where he repeatedly stabbed three men, killing them and leaving behind what Brown described as a horrifying crime scene.
He then made his way to a nearby sorority house, whose members heard loud and aggressive knocking on the door for at least a minute. But no one from the collegiate women's organization answered, Brown said.
He said that shortly afterward, witnesses reported seeing Rodger shoot three young women standing outside the sorority house. Two of those women, students Katherine Cooper, 22, and Veronica Weiss, 19, died.
Driving off to a nearby delicatessen, Rodger got out of his car, entered the deli and shot dead 20-year-old UCSB student Christopher Michael-Martinez, Brown said. Police responded and Rodger fled in his car.
He shot at pedestrians as he drove around Isla Vista, traded fire with police and struck bicyclists on two occasions before he crashed his car and officers found him with an apparently self-inflicted gunshot wound to the head, Brown said.
Richard Martinez told reporters that his son Christopher was an English major who wanted to go to law school.
"Why did Chris die? Chris died because of craven, irresponsible politicians and the NRA," Martinez told reporters outside the Santa Barbara County Sheriff's Office, close to collapsing from emotion. "They talk about gun rights, what about Chris' right to live? When will this insanity stop?"
The National Rifle Association, or NRA, supports the