"We've set up blue-ribbon panels; we've set up community panels; we've set up conversations, walk-and-talks with our police department and our community," he said on NBC's "Meet the Press" Sunday. "And we're moving towards a trustful relationship between city hall, the police department, and our community."
Triplett declined to comment on whether Martin did anything wrong.
"We from day one that we were seeking justice when the demonstrations came to the City of Sanford, that they wanted Mr. Zimmerman to sit in front of a jury of his peers. That's what's taken place. And they have spoken. They've listened to both sides of it," he said.
The Rev. Al Sharpton, who was also on Sunday's show, said there are grounds for civil rights charges in the case.
"The trial happened, the verdict came in. That does not exhaust the legal options of this family, and the bigger community issues of civil rights," Sharpton said.
He also disagreed with the verdict.
"We now have a position on the books, in the state of Florida, where an unarmed teenager who committed no crime can be killed and the killer can say self-defense," he said. "That is dangerous. That is an atrocity. And I think that must be addressed."
Celebrity Families of 2014 [PHOTOS]