I'm surprised that atheists reflect much on their regrets, as whatever happens is all based on our environment and experiences, so I would have though everything falls in the category of 'it is what it is.
I wonder why you have regrets.
Well surprisingly - perhaps to you - most atheists probably reflect just as much about life and what they do in such as the religious might - perhaps even more so since they have to do more thinking rather than accepting some answers from others. Guilt and shame might be valuable to many if it wasn't such a drag and hindered their future lives. Perhaps it is better just to assimilate experiences and move on. And perhaps forgiveness from others is better too rather than hatred, revenge or ostracism.
We all have regrets since I doubt there is anyone on the planet without any.