Joe and Claryce Holcombe have alleged in their claim that the Air Force's actions "directly caused this horrific tragedy," as they failed to follow their own policies by not reporting the shooter's criminal history to the FBI.
Mr Holcombe told CNN: "We want to see this sort of thing not happen again, and I think if the Air Force had have done its job properly this wouldn't have happened."
Crystal Holcombe, 36, and three of her children, Greg, 13, Emily, 11, and Megan, 9, were all killed, while her husband John Holcombe, was among the massacre's few survivors.
His parents, 60-year-old Bryan and Karla Holcombe, 58; brother, 36-year-old Marc Holcombe, and Marc's 18-month-old daughter, Noah, were also killed when Devin Patrick Kelley, opened fire at the First Baptist Church in Sutherland Springs, killing 26 people and injuring 20.
The family's claim states: "Although (Kelley) undoubtedly 'pulled the trigger' that resulted in injuries and death of J.B. Holcombe and others, the failures of the US Air Force, and others, allowed the shooter to purchase, own and/or possess the semiautomatic rifle, ammunition and body armour he used."
On Wednesday, the Air Force released a statement which said that it's "review of its reporting processes to civilian law enforcement in the Devin P. Kelley case has prompted immediate actions to correct reporting deficiencies and prevent future occurrences".
The review also found the error in the Kelley case was not an isolated incident and similar reporting lapses occurred at other locations.
If Kelley's conviction had been passed to the FBI, as required by law, the gunman wouldn't have been able to legally purchase some of the weapons he used in the deadly attack.
Air Force Security Forces has already implemented several corrective measures and, according to its statement, "remaining actions will be completed in the next few weeks".
