In this instance (as with the OJ Simpson case) blacks and whites tended to see things very differently. These differences showed that African Americans generally tend not to trust the police and to see them as oppressors. By contrast, white Americans see the police (at least when the police are dealing with African Americans) as fair and unbiased defenders of the good people of society.
To blacks, King's case was another, high-profile, example of how the police brutalize African Americans unfairly. At that time, there were many accounts in the media of African Americans being pulled over simply for "driving while black." That sort of thing caused a great deal of resentment among African Americans and the King case gave them even more reason for anger. When the officers were acquitted, it seemed like proof that the justice system was rigged against African Americans.
Whites, by contrast, (and of course this is an overgeneralization) saw the officers as men who were just doing their jobs. They blamed King for being drunk, for fleeing the police, and for resisting arrest. They saw what happened to him as fair and appropriate. This showed their greater faith in police and in the justice system.