Bottles

I have had to give in to breast feeding. Georgia just wasn't getting enough nourishment from me. Her fontenelle was sunken and she was always hungry. So I started her on bottle feeding yesterday and even though she had had a full breast feed she drank 250ml of formula.
is it admitting defeat? I think it hard to let go as a parent and know that you can't do it on your own. But for the health of my beautiful little girl I had to bite the bullet.