English is not my first language, but the first sentence (I accept my fault) doesn't sound very natural to me. I have looked up the word accept in several dictionaries and haven't found any similar example. It is often used with responsibility or blame. Another word that seems to convey the same meaning is admit, but that sounds a little formal and serious. What is the most natural way of saying that you are responsible for something wrong? Personally, the second sentence (I accept it is/was my fault/mistake.) sounds more natural to me.