"The loss of 20 first-graders and six educators would shake any community to its core,” the appeal stated. "Ours had to grapple with the manner in which those lives were lost."
The families have accused Remington of marketing a weapon it knew was a state-of-the-art "assault weapon designed for combat" to civilians.
"Children and teachers were gunned down in classrooms and hallways with a weapon that was designed for our armed forces and engineered to deliver maximum carnage," the appeal continued.
A judge dismissed the lawsuit earlier this year, saying the gun manufacturer is protected by federal law.
Attorney Josh Koskoff, who is representing the families, said that the Connecticut state supreme court may want to take a fresh look at the marketing of a weapon.
"There is no precedent for this case in Connecticut," Koskoff said.
One young victim's father, Ian Hockley, said he is "bringing this appeal to prevent the next mass shooting."
Hockley's son Dylan was shot at least five times.