One of the victims apparently recognized 25-year-old Julian Collender as the suspect armed with a semiautomatic handgun.
Police said Collender was shot once in the chest after coming out of his home when he was confronted by officers. He was transported to a local hospital, where he later died.
Police are not saying what happened right before the shot was fired.
The Orange County District Attorney's Office is investigating the shooting.
"I'm mad as hell," said Collender's father, Richard. "I think the Brea Police Department shot and killed him without any kind of reason."
Brea police Sgt. Bill Smyser said Collender "took some cash, some iPods and keys."
"There was a gun involved in the initial robbery, so there was concern by the officers about that," Smyser said. "I can't speculate what was going through the officers' minds."
Smyser said he didn't know if the gun was seen at the home.
"He doesn't even know if my son was armed, and my son, to my knowledge, never had any weapon," Richard Collender said. "He has never been in trouble."
Police said they found a handgun inside the home matching the description of the weapon used in the robbery, as well as a shotgun.
Authorities also said additional suspects may have been involved in the crime.
"My son didn't need money," Richard Collender said. "He lived at home. He was collecting unemployment. I would give him money."
Documents show his only past trouble were some traffic citations.
A charge of drinking or possession of alcohol in public was dismissed in February.
No one else was injured in the incident.
Anyone with information about the robbery or officer-involved shooting is urged to call the Brea Police Department at (714) 990-7677.