Trayvon Martin's parents: This wasn't "God's plan"

Updated at 8:14 a.m. ET

(CBS News) Trayvon Martin's parents spoke on "CBS This Morning" Thursday and rejected George Zimmerman's reasoning that shooting the Florida teenager to death last February was "God's plan."

The neighborhood watch volunteer charged with second-degree murder appeared on Fox News Wednesday night and said he acted in self-defense when he shot Martin. He also apologized to Martin's parents.

"I simply really don't know what God George Zimmerman's worshipping because there's no way that the God that I serve had in his plans for George Zimmerman to murder my son," Martin's father, Tracy Martin, told Norah O'Donnell.

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Martin's mother, Sybrina Fulton, doubted that Zimmerman's apology was sincere.

"I have a hard time accepting it because he also said that he doesn't regret anything that he did that night, and I don't think God would have him in his plan to murder an innocent child," Fulton said.

"I just think it's a tragic situation, and I hope it's the most difficult thing I'll ever go through in my life," Zimmerman said.

During the interview with Fox News' Sean Hannity, Zimmerman described the moment he came face-to-face with Martin and fatally pulled the trigger.

"He said, 'You're going to die tonight [expletive],' and took one hand off of my mouth, and I felt it going down my chest towards my belt and my holster, and that's when I didn't have any more time."

Sitting next to his lawyer, Zimmerman appeared calm as he denied ever pursuing Martin.

"I was going in the same direction as him to keep an eye on him so that I could tell the police where he was going," Zimmerman said.

The 28-year-old insisted self-defense was his only motivation.

"I'm not a racist, and I'm not a murderer," Zimmerman said.

When asked about regrets, Zimmerman said he had none.

But later he appeared to backtrack, looking directly into the camera to clarify himself.

"I do wish that there was something, anything, I could have done that wouldn't have put me in the position where I had to take his life," Zimmerman said.

Zimmerman lawyer Mark O'Mara said there were no ground rules for the one-hour interview though he did jump in when a question came up about whether Zimmerman and his wife lied to the court about their finances.

As for Martin's parents, Zimmerman had this message:

"I am sorry that they buried their child. I can't imagine what it must feel like, and I pray for them daily."

Zimmerman remains out on $1 million bail. His attorney said his trial could be more than a year away.