Dana and Mark Gerstle had planned to talk about how Zimmerman, who successfully pleaded self-defense in the shooting death of unarmed black teenager Trayvon Martin in Sanford, had helped them and their two children get out of their sport utility vehicle after they crashed recently.
But Zimmerman's attorney, Mark O'Mara, told ABC News the Gerstles' "voices were trembling" when they told him anything positive they said about Zimmerman "would be toxic" because of the negative reaction to Zimmerman's acquittal.
O'Mara said holding a formal news conference would have helped the family "get back to a normal life."
"But they called today and said they were more worried about blowback from saying anything that would be favorable to George, and decided they did not want to do any media," O'Mara said.
Zimmerman and another man extricated the Gerstles and their children from their Ford Explorer SUV after it left a highway in Sanford and rolled over last Thursday, the Seminole County Sheriff's Office said.
The department said in a statement the Gerstles "expressed to us that they are not comfortable doing media interviews at this time and they continue to ask for privacy."
Zimmerman had not been seen in public since his acquittal until he showed up at the scene of the traffic accident, in which no injuries were reported.