I personally wouldn't tell my daughter I'm sorry I raised my voice at her, because I'm not. I would disagree with your contention "we all know its terrible to raise your voice at kids." Sometimes you hurt your kids' feelings. I don't feel bad about it.
My parents raised me with (what I see in hindsight to be) a healthy balance of a wide variety of emotions, all of which I had to learn about eventually. As a result, I was consistently viewed by adults as having a more advanced emotional structure than my peers all through school. Why? Because my parents didn't hide anger or displeasure or disappointment just as they didn't hide joy or pleasure or pride in me.
They weren't perfect by any means, but as I look back on it, their introduction of the wide range of emotions and behaviors (including anger and violence) taught me how to handle these naturally occurring phenomenon in a responsible manner. (You wouldn't believe this, there is actually violence in the real world. You should've seen how shocked my wife was at the world when we moved to Cleveland, Ohio for my first job out of uni - turns out her upbringing had protected her from the mere existence of the level of violence, racism and hatred we saw there.)
So the bottom line is, embrace these opportunities as learning experiences. I'm not suggesting you consistently raise your voice, all day, every day. But when you do on occasion, (I feel) you're making your child stronger in the long run. Yes she may start to cry because mommy or daddy raised their voice. That's part of life. It has happened before, it will happen again, it will happen from a wife variety of people throughout his or her life. (She perceives all voice-raising as yelling and screaming, which is not necessarily the case, it's important for her to learn the difference between different magnitudes and durations of yelling and what implications they have.)
Like all posts on this site, this is entirely my perception gained by self examination both as a parent and as a child. If someone has a system that contradicts this (which millions will have, I'm sure) please know that I respect what works for your delicate balance between you and your kids, and what relationships you had between you and your parents, and I would appreciate the same.