The way we usually say this is:
This is my fault.
Also, in your sentences, you should rephrase the first part. Instead of:
I always forget your book to bring...
I always forget to bring your book. This is my fault.
Even in English, sometimes people use the Latin phrase mea culpa to indicate fault. It's usually regarded as a way to express sheepish embarrassment:
I always forget to bring your book. Mea culpa.
Also, there are other, more informal ways to indicate fault in everyday conversation. I like this one:
I always forget to bring your book. My bad.