In fact you can say both "C'est ma faute" or "C'est de ma faute".
The first one is considered more correct but you will hear both in French .
It is an idiomatic 'de' so hard to justify...
C'est ma faute, c'est ma faute, c'est ma très grande faute = Mea culpa, mea culpa, mea maxima culpa
Hope this helps!
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