"The change that we hope to affect is with the law," Fulton said. "We want to make sure any teenager who is walking down the street wont' be killed, that they will make it home safe."
"Hopefully, we can find some positive, some bright side out of all of this," she said.
The parents did not say whether they may file a civil lawsuit.
Benjamin Crump, an attorney for Martin's family who also appeared on "Anderson Cooper 360," said they are hoping for a federal civil rights investigation into the teenager's death.
He said they were pleased by the charges brought against Zimmerman because they felt it got to the heart of the allegations.
But he said he did not believe the police were aggressive with the shooting investigation, appearing to take Zimmerman's word for it.
"Not only did (Zimmerman) profile Trayvon Martin, the police profiled Trayvon Martin," Crump said.
'Forgiveness takes time'
Earlier Thursday, in interviews on the three network TV morning news programs, Martin's parents assailed the verdict and the Zimmerman defense team's argument that the killing was in self-defense during an attack by the unarmed teenager.
Fulton told "CBS This Morning" she was "in a bit of shock" after the verdict. "I thought surely that he would be found guilty of second-degree murder," she said.
On NBC's "Today," Fulton said the case is "sending a terrible message to other little black and brown boys -- that you can't walk fast, you can't walk slow. So what do they do? I mean, how do you get home without people knowing or either assuming that you're doing something wrong? Trayvon wasn't doing anything wrong."
Speaking to ABC's "Good Morning America," Martin added that he and Fulton did not find the verdict fair, "and of course it's devastating."
"Today" asked them whether they may forgive Zimmerman, the 29-year-old neighborhood watch volunteer.
"Forgiveness is like a healing process. Forgiveness takes time," Martin responded. "The Bible says that you have to forgive and forget, but also the healing process is a long process and the forgiving process is a long process."