Hi Olga,
You do not need to use "about" with "regret".
Examples:
If you use it as a verb, you may write:
I regret telling you my secret.
I regret my actions.
In these sentences, "regret" means the ACTION of feeling sorry and wishing something was done differently.
If you use it as a noun, you may write:
I would like to express my regret.
Life is full of regrets.
In these sentences, "regret" means a state of BEING sorry that something was not done properly.
Hope this helps.
Cheers,
Lance