I'm not a coward, I've just never been tested
I'd like to think that if I was I would pass
Look at the tested and think "there but for the grace go I"
Might be a coward, I'm afraid of what I might find out
—"The Impression That I Get" by The Mighty Mighty Bosstones
We can't change the past. When someone does something wrong, the act of saying "Sorry" doesn't help. Actually feeling sorry doesn't help, either. Saying or feeling sorry can only help as part of a process that decreases the measure of the wrong across the multiverse. We can't change our past, but we can update on its evidence—use the memories and records of it as input to a function that changes who we are in a way that makes us perform better in the future (which is somebody else's past). And we can create timeless incentives: if people know that history (and the court system) has its eyes on them, they might do things differently than they would if they knew no one would ever hold them to account.
The update part is more important than the timeless-incentives part. The first duty is to investigate exactly what happened and why. If you can learn the causal graph, you can compute counterfactuals: if this-and-such detail had been different but everything else had been the same, what would have happened instead? If you can compute that if this-and-such detail had been different, then something better would have happened, then you can make advance plans and take advance precautions to make sure the analogous detail takes a more favorable value in analogous future situations.
And, yeah, in addition to making better plans, you can also do incentives (to timelessly influence the past) and restitution (to try to make up for the past): punish the guilty, give them bad reputations, make them pay cash damages to their victims, &c. But you have to get the facts first, so that you can compute what punishments, reputations, and restitution to impose.
You must thoroughly research this, not only when your actions participated in disaster, but also when your actions participate in a near-miss "warning shot." It is not the case that all's well that ends well when you're playing for measure in many worlds. If you were in a situation where disaster had probability 0.5, and disaster didn't happen, that just means this copy of you got lucky.
And just because this copy of you doesn't have blood on her hands, doesn't mean you're innocent.
Wanting a fair trial isn't the same thing as claiming to be innocent. It's wanting an accurate shared account of exactly what you're guilty of.