Zimmerman, 29, was found not guilty Saturday night of the shooting death of the 17-year-old in February 2012.
In an appearance on ABC's "This Week," Crump said the family is trying to make sense of the verdict and are considering a civil suit against the man.
"They are going to certainly look at [a civil suit] as an option. They deeply want a sense of justice. They deeply don't want their son's death to be in vain," he said. "I mean, they are still in disbelief about his death and now they're in disbelief about this verdict. It's just one of the things they have to deal with -- they're in church this morning, praying and turning to god, a higher authority, to make sense of it all."
Crump said the family is focusing their energy on the Justice Trayvon Martin Foundation, which, among other things, is working to amend the "Stand Your Ground Law," the law Zimmerman used as a defense in the case.
"They had to depend completely on the justice system and pray that it would work for them as it worked for everybody else," Crump said. "And so the one thing they can control is this foundation. And Tracy and Sybrina have been trying to do that work so they can make sure there are no other children who get killed as a result of senseless gun violence."