"The culture of the Los Angeles Police Department has been transformed," Erwin Chemerinsky, a professor and the founding dean of the School of Law at the University of California-Irvine, told KABC-TV.
Bratton has since gone on to advise the police forces of other major cities including London, where he now serves as a consultant to police after he city's spate of riots last year.
But 20 years after the 1992 acquittal of the LAPD officers ignited days of deadly riots in Los Angeles, Jackson said, the shooting of Trayvon Martin shows that race relations are still far from where they should be.
The NYPD, for example, has come under increasing criticism for its stop-and-frisk program, in which it detained more than 685,000 people in 2011, the majority of them young blacks and Hispanics, according to the New York Civil Liberties Union. That's up from about 97,300 stop-and-frisk incidents back in 2002.
Jackson said the persistent present-day bias is also reflected by the 8,000 blacks killed in the United States each year.
"It isn't just the police," he said. "Our concern now, of course, is too much racially-targeted violence.
"We had a redemptive moment with President Barack Obama's election," Jackson said.
But contrary to King's "resounding appeal for us to get along," he said, "it seems that we're not."
ABC News radio contributed to this report.