(CNN)The family of Michael Brown, the teen killed last year by Ferguson police officer Darren Wilson, will file a civil wrongful death lawsuit in the case "very shortly," attorney Anthony Gray said Thursday. Neither he nor attorney Daryl Parks would say exactly when the suit would be filed, but they said that they disagreed with the grand jury's and the Justice Department's decisions not to charge Wilson in the shooting. "They have accepted (Wilson's) self-defense," Parks told reporters. "We do not accept his self-defense." The slain teen's parents, Michael Brown Sr. and Lesley McSpadden, were in attendance at the news conference but did not speak on advice of their attorneys, Parks said. "The last 24 hours have been tough for them," he said. Word of the lawsuit comes a day after the Justice Department determined there was not sufficient evidence to charge Wilson in Brown's death but found in a separate investigation that the Ferguson Police Department showed a pattern of racial bias. Brown Sr. and McSpadden released a statement Wednesday saying they were disappointed that Wilson would not face charges, but, they added, the federal report on the police department could provide a silver lining. "We are encouraged that the DOJ will hold the Ferguson Police Department accountable for the pattern of racial bias and profiling they found in their handling of interactions with people of color," the statement said. "It is our hope that through this action, true change will come not only in Ferguson, but around the country. If that change happens, our son's death will not have been in vain." In November, a grand jury cleared Wilson and, in an uncharacteristic move in grand jury proceedings, the prosecutor released all the evidence that was considered. Gray said the civil lawsuit will rely on "pretty much the same evidence," but it will be cast differently. The jury in the civil lawsuit will be asked to make a determination based on a lower burden of proof -- by a preponderance of evidence, rather than beyond a reasonable doubt, Parks said. Summing up the crux of the Brown family's case, Parks said, "There were other alternatives available to (Wilson). He did not have to kill Michael Brown."
Attorney says jury in civil lawsuit will make decision based on lower burden of proof . Word of the lawsuit comes a day after Justice Department declines to charge Darren Wilson .