OH NO! This is so terrible!
It really isn't your fault. Don't beat yourself up. Sometimes we leave the door cracked while we put the trash out and there have been times that Hobbs has slipped out, we come back in, shut the door with him still outside, and don't even realize that he is outside! It happens all the time.
Go knock on neighbors door and tell them to look out for her. Make flyers and put them in people's mailboxes and on telephone poles. Call all your vets in the area and shelters and humane societies. Someone will find this little girl. Poor thing