But at a news conference Thursday, Police Chief Rick Dinse said their two goals had been met: Elizabeth was found safe and her captors were in custody.
Members of the Smart family had criticized the department for dismissing Brian Mitchell, the self-styled preacher who was arrested along with his wife Wednesday.
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Dinse acknowledged investigators were slow to release a sketch of Mitchell, who Elizabeth's sister had suggested was the abductor.
"Hindsight is 20-20 vision. If we had to go back over it again, I think every one of (our investigators) would say, 'I wish we had gone public with that … earlier,'" Dinse said.
Salt Lake City Mayor Rocky Anderson proposed an independent review of the way the case was handled "just to resolve any questions that may be lingering."
In a wide-ranging news conference with FBI agent Chip Burrus, Dinse said Mitchell fancied himself a polygamist, although he refused to say if 15-year-old Elizabeth Smart was sexually assaulted.
The details of Elizabeth's captivity are gradually becoming clear. Dinse said Mitchell acted alone in snatching the girl at knifepoint from her bedroom June 5.
Mitchell, his wife and Elizabeth lived at a remote campsite for two months in the rugged foothills above the Smarts' house, spent time in Salt Lake City and then took a bus to San Diego.
Mitchell and his wife, Wanda Barzee, were arrested Wednesday after returning to Utah. Two couples who recognized Mitchell from the television show "America's Most Wanted" told police he was walking along a street in the Salt Lake City suburb of Sandy with a girl who turned out to be Smart.
Police fielded more than 16,000 tips in their search for Elizabeth Smart, but it was just one — from Elizabeth's younger sister — that really mattered in the end.
In October, 9-year-old Mary Katherine Smart recalled that the intruder who took her older sister from their shared bed most likely was Mitchell, a one-time family handyman then known only as Emmanuel.
But police focused on Richard Ricci, who died Aug. 30 of a brain hemorrhage and had insisted he had nothing to do with Elizabeth's disappearance.
Dinse acknowledged that half of his task force worked on Ricci while the other half pursued all other leads in the case. On Thursday, he said Ricci was not involved in the Smart abduction.
Ricci's widow is demanding an apology from police, whose suspicions led to Ricci's arrest on parole violations. He died in jail in August.
Ricci received a white Jeep from Ed Smart for doing handyman work at the Smart home. After Elizabeth disappeared, Neth Moul, Ricci's mechanic, told The Associated Press that Ricci put about 1,000 miles on the car's odometer in nine days.
Police said Ricci never adequately explained the additional mileage or mud caked on the car.
In addition, because Ricci had worked in the Smart house, he was thought to know the home's interior. Elizabeth's alleged kidnapper entered through a kitchen window, told her to get her shoes and left with her, police said.
Prior to Mitchell's emergence as a suspect, Ed Smart had consistently said he believed Ricci was somehow involved in the girl's disappearance.
Asked Thursday if police performance was lacking, Ed Smart said, "I believe that some mistakes have been made, but I know that they were trying."
"We learn by our mistakes," he said. "We don't have professional kidnap policemen, so we do our best."
Elizabeth is reported to be healthy, but not unchanged by her ordeal.
"There is clearly a psychological impact that occurred at some point," Dinse said Thursday. "There is no question that she was psychologically affected."
When stopped by police, she readily lied about her identity and said the two drifters were her parents. The 15-year-old was nervous and agitated when asked to remove her sunglasses and gray wig and never asked about her family once the truth emerged.
Smart told police her name was "Augustine" and that her cheap black sunglasses protected her eyes while they healed from surgery. When they asked why she wore a wig and T-shirt for a head scarf, she became angry and upset.
Handcuffed and loaded into a separate police car from Mitchell and Barzee for the ride to the station, Smart began to cry.
"We kept telling her, do this for your family, do this for yourself. Do the right thing — we know you're Elizabeth Smart," said Sergeant Victor Quezada.
Smart responded with a biblical quote, "Thou sayest."
The teen may have picked up the religious reference from Mitchell, a 49-year-old panhandler and self-proclaimed prophet for the homeless who called himself Emmanuel. The trio were seen wearing long white robes, with Barzee and Smart often veiled and following silently.
Mitchell, who didn't have a lawyer Thursday, was being held at the Salt Lake County jail on suspicion of aggravated kidnapping. Officials said he wasn't responding to interview requests.