(CNN) -- A Louisiana man who spent 15 years on death row for a murder he did not commit was released Friday from prison in an exoneration brought about by the Innocence Project.
"It's been a long journey," Damon A. Thibodeaux, 38, said during a news conference with his lawyers. "It's people like y'all who give people like us a chance."
Thibodeaux, who was convicted after falsely confessing to having raped and murdered his 14-year-old step-cousin, said he hopes law enforcement will learn from his case.
"Make sure you have the right person before you start a process of executing someone," he said. "Because it costs a lot of money to go back and look at all of these cases again. If it's done right the first time, you shouldn't have to do that."
Thibodeaux described as "surreal" his walk earlier in the day out of Louisiana State Penitentiary. "It's not something you can prepare yourself for, because you've been living in those conditions for so long."
Asked how he felt, Thibodeaux did not hesitate. "Free," he said. "I feel free. I feel free."
Initially, he said, he felt like giving up, but resisted the temptation. "The minute you give up completely is the minute you die," he said. "Period."
Thibodeaux said that he was looking forward to "peace and quiet ... just concentrating on putting my life back together and moving forward."
His court-ordered release came after DNA and other evidence exonerated him. Jefferson Parish District Attorney Paul Connick Jr. agreed with Thibodeaux's lawyers that he had confessed to something he did not do.
Connick "joined the Innocence Project and Thibodeaux's other counsel in agreeing to overturn Thibodeaux's conviction and death sentence after his confession to police was determined to be false," the district attorney said in a statement.
"This is a damn good day at the office," said Denise LeBoeuf, director of the ACLU Capital Punishment Project, who has represented Thibodeaux since 1998.
The case points to the need to abolish the death penalty, she said. "It doesn't make us safer; it makes the pain of murder worse; and if we can't figure out how to have a death penalty that doesn't put innocent men on death row and innocent women on death row across the country, then we don't deserve to have it. It is a human rights violation. We need to end it now."
Thibodeaux was convicted of killing his relative, Crystal Champagne, whose body was found on July 20, 1996, a day after she left her apartment to go to a nearby supermarket.
He was among a number of people who were interviewed by police. After some nine hours of interrogation, "he provided an apparent confession to raping and murdering the victim," the ACLU said in a news release. Primarily on that basis, Thibodeaux was convicted and sentenced to death in October 1997, it said.
A decade later, his legal team gave evidence to the district attorney of Thibodeaux's innocence and an investigation -- which wound up involving hundreds of thousands of dollars worth of DNA testing, forensic evidence and interviews -- got under way.
"The probe confirmed that Thibodeaux's confession was false in every significant aspect," the ACLU said.
Since 2000, six people have been released from Louisiana's death row after being exonerated; in that time, three people have been executed, it said.
"What we were doing was searching for the truth," said Barry Scheck, co-director of the Innocence Project, which is affiliated with New York's Benjamin N. Cardozo School of Law. "We hope that justice is done and we find the person who really committed the crime."
He said Thibodeaux was the 300th person exonerated through DNA testing.
Asked what might have led Thibodeaux to confess, Scheck said, "That is something that we're studying and is part of the lessons to be learned here. That's not one of the things that I think is probably appropriate for us to discuss at the moment."
The case points to the need for police to videotape interrogations, according to Scheck. Had that been done in this case, "we wouldn't be sitting here today," Scheck said. "It's a simple thing to do and it's sweeping the country."