On NBC's "Today" show, Sybrina Fulton questioned whether jurors looked at the shooting from her son's point of view.
"He was a teenager. He was scared. He did run," Fulton said, who added that she believes the justice system failed her son.
"We didn't get the verdict we wanted because we wanted him to be (held) accountable."
Martin's father, Tracy Martin, expressed disbelief in the verdict handed down Saturday by a six-woman jury following a three-week trial in central Florida.
"We felt in our hearts that we were going to get a conviction," Martin said. "We felt that the killer of our unarmed child was going to be convicted of the crime he committed."
On ABC's "Good Morning America," Tracy Martin said he felt the jury did not get a chance to get to know the teen. "They didn't know him as a human being," he said.
Martin's parents said they still believe Zimmerman, who identifies himself as Hispanic, racially profiled their son.
"Obviously, any time you have a person that makes an assumption that a person is up to no good, that's some kind of profiling," Martin said. "Was he racially profiled? I think if Trayvon had been white, this never would have happened."
Martin's parents said they support the federal government looking into the case. The Justice Department announced Sunday it plans to review the case to determine whether federal prosecutors should file criminal civil rights charges now that Zimmerman has been acquitted.
Zimmerman, who was charged with second-degree murder, claimed he shot Martin in self-defense.
Martin's mother said she believes the verdict sends a "terrible message to other little black and brown boys."
"They can't walk fast. They can't walk slow. So what do they do? How do they get home without people assuming you are doing something wrong?," Fulton said.
Fulton told "CBS This Morning" her son was not a burglar.
"He simply went to the store and was headed back home," she said. "And for somebody to look at him and perceive that he was a burglar, that was the problem that initiated everything."
The parents' attorney, Benjamin Crump, didn't rule out a civil lawsuit against Zimmerman in response to a question from CBS's Charlie Rose.
"We'll look at all legal options. Right now, we'll ask the Department of Justice to answer ... `Can a private citizen with a gun profile and follow our children home?"' Crump said.
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