The Hillsborough report released this week revealed the shocking cover-ups by members of South Yorkshire Police and other organisations for the past 23 years.
Moyes has paid tribute to the families for pursuing the matter in order to exonerate their loved ones and claim justice for them after blame was shifted to the supporters by police after the incident.
He told reporters: "I think everybody was shocked and saddened by what happened and still are. Everybody is stunned by what they're hearing about it now.
"Great credit goes to the families for pursuing this. It has been a terrible travesty of justice.
"In the end, if any of us lost someone in that situation, we would feel aggrieved. I think I'd be more disappointed in the people who we trust in authority that have not come out and been forward enough to say they got it wrong and made mistakes.
"Good people stand up, hold their hands up and accept mistakes. For it to take 23 years is nothing short of scandalous."
The Scot feels the disaster brought the City of Liverpool together as both supporters of Everton and the Reds stood united in grief and now have closure over the findings of the report and the justice for the victims.
He added: "I wasn't here when the disaster happened - I was a player at the time.
"I'm sure then that everyone in the city stood together as one and now we stand shoulder to shoulder with the families of the bereaved, who have had to put up with this, and congratulate them for persevering and getting the outcome they all believed in."