I made a mistake.
Please accept my apologies.
I'm sorry. I didn't mean to . . .
(I'm) sorry. I didn't realize that . . . .
Prefacing bad news
I'm sorry (I have) to tell you this, but . . .
I hate to tell you this, but . . .
I don't know how to tell you this, but . . .
I have some bad news.
(Formal) written apologies
We regret to inform you that . . .
Regretfully, . . .
Unfortunately, . . .