Officers responding to a disturbance at 3 a.m. Friday morning said Doucet was naked and behaving erratically.
They said he repeatedly punched them and tried to take one of the officer's guns.
Friends planned to hold a candlelight vigil for Doucet Sunday night.
"It's just everybody's loss. We feel devastated by this. We also feel it is a tragedy that should not have happened," said Earl Ofari Hutchinson with the Los Angeles Urban Round Table.
The Los Angeles Police Protective League said it is disappointed that community leaders are immediately blaming the LAPD.
The president of the LA police union said in a Saturday statement that the officers were "fighting for their lives" in that incident.
Two officers were treated for injuries to the face following the reported fight.