I admitted I was alcoholic years ago.
The acceptance part (for me) is acknowledging the fact that I can no longer continue to live that way. Once I accepted that, I had to do something about it.
Another way to state it is that I embraced it. It became my reality. I could either go through the rest of my life drinking and continuing to spiral out of control or I could stop drinking and right myself knowing that the only way to do so was to never allow alcohol (never give it another chance) to interfere with my life again. And obviously, there is only one certain way to ensure this. Never drink again.