"I'm not an extreme liberal," Payton said in an interview with USA Today. "I find myself leaning to the right on some issues. But on this issue, I can't wrap my brain around it."
"If this opinion in Louisiana is super unpopular, so be it." Payton said.
He added, "I hate guns."
Smith, a defensive end who played a key role in the Saints' 2009 Super Bowl victory and made the Pro Bowl in 2006, was fatally shot following a fender bender in New Orleans's Garden District. He was pronounced dead on the scene. His wife, Racquel, was also shot and taken to an area hospital for treatment, police said.
On Sunday morning, police announced the arrest of Cardell Hayes, 28, in connection with Smith's death. Hayes allegedly shot Smith and Racquel after he rear-ended their vehicle with his Hummer. Smith and Hayes "exchanged words" and Hayes "produced a handgun and shot Smith multiple times," police have alleged.
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Hayes's attorney, John Fuller, who has not returned PEOPLE's request for comment, has said Hayes was "not the aggressor."
Payton told USA Today": "Two hundred years from now, they're going to look back and say, 'What was that madness about?'"
He added, "The idea that we need them to fend off intruders … people are more apt to draw them [in other situations]. That's some silly stuff we're hanging on to."
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Payton spent Saturday evening participating in an auction for a charity event at the House of Blues. Returning home after midnight, he learned of Smith's death, which occurred only about eight blocks from Payton's home. He drove to the scene around 5:45 Sunday morning. He then spent several hours at the hospital where Racquel underwent surgery.
After returning home, Payton researched the gun used in Smith's killing.
"It was a large caliber gun. A .45," he said. "It was designed back during World War I. And this thing just stops people. It will kill someone within four or five seconds after they are struck. You bleed out. After the first shot [which struck Smith's torso], he took three more in his back."
"We could go online and get 10 of them, and have them shipped to our house tomorrow," he added. "I don't believe that was the intention when they allowed for the right for citizens to bear arms."
Smith was killed just weeks before he was to join the Saints' coaching staff as an intern.
"I don't know how he felt about guns," Payton said. "I know he loved this city. And I know he was going to be a heck of a coach. He had such a presence about him. Not only would he have made the transition to be a great defensive line coach, he had all the tools to become a head coach.
"We just don't get to see those chapters. All the chapters before now were great. But it's sad that we won't see the next chapters."