"I accept my fault." vs "I accept it was my fault."

"I accept my fault" implies that you are admitting that you were at fault at a given point.

As defined in Oxford English Dictionary:

An unattractive or unsatisfactory feature, especially in a piece of work or in a person's character.

"I accept it was my fault" indicates that a specific result was produced because of your mistake. It should also be noticed that, here, you might be trying to say that the said result was not caused by someone else's error and that you were responsible. The previous statement signifies characteristic while this one hints responsibility.

Another definition of the word "fault" in Oxford English Dictionary:

Responsibility for an accident or misfortune.

Source: https://www.lexico.com/en/definition/fault