DON'T DO THAT!!! What does it add to what your saying? Yes, you made a mistake. Yes, you're sorry. Yes, you'll make up for it. What can "I'm stupid" possibly add in value to that line of conversation? First of all, it doesn't have anything to do with being stupid, so it's not true, it's just modeling self scorn.
Nothing will scar your kids for life if you accidentally do it now and then, but still, DON'T do that! I'm saying this, because my mom does it, and I HATE IT. I literally cringe every time I hear her saying she's stupid. She thinks it's "humble and self effacing". Only as an older, confident person who overcame the overboard humble act she passed down to me can I now see how awful that is. I got used to her saying it when I was little (yuck). I've since read many places you should not criticize yourself in front of your kids if you want them to be confident about themselves.
Whenever my mom calls herself stupid when we visit, my kids look stung, and say, "no your not, grandma!" Then finally I heard my son say "I'm stupid" about himself. It almost brought me to tears. I said, "You are not stupid, please do not say that about yourself, you have a wonderful brain that God gave you and it's not nice to say that about yourself." He liked the attention and did it a few more times, but I did get firm with it. The kids are not allowed to say that about anyone, including themselves. And I don't do it.
Yes, I apologize and admit mistakes all the time, and yes I left my wallet on top of the car and drove away three times in one week, but I don't call myself stupid. Your kids don't like to hear that. How did you feel when your daughter said it? That's all you need to know.