There is a little difference in french between the two sentences, with or without de.

c’est de sa faute

That is more or less he is responsable for that or that has occured because of him

C’est sa faute

It can be a familiar form of c’est de sa faute, which if often used by children. Else, it means that a fault has been commited and the fault is his one

IMHO a better translation would be

I think this happened because of him

de is not necessary in the sentence. The good way to say the sentence would be to simply say:

J’estime que c’est sa faute.

This formulation has been used for instance by Victor Hugo’s character in Les Misérables, Gavroche:

On est laid à Nanterre,

C’est la faute à Voltaire,

Et bête à Palaiseau,

C’est la faute à Rousseau.

It does not mean using de before sa faute is wrong. The two sentences do have the same meaning. But it is informal. In Le Bon Usage, page 293, you can read that some grammarians would prefer not to use such a form:

Certains grammairiens condamnent particulièrement C’est de la faute de ta mère. Il est préférable, dans l’écrit, d’éviter ces de successifs.

But no one will ever tell you anything if you are using it to be honest. Most French people say de sa faute without even thinking about it.

De is not necessary and both are correct :

C’est de ma faute.
C’est ma faute.

Grevisse says only C’est ma faute is mentioned by Littré, and by Le Dictionnaire de l’Académie française . He adds though that the phrase with de is often found in literary language. Le trésor de la langue française (II B) gives the de form as colloquial.

♦ Fam. C’est de ma (ta, sa, etc.) faute. Même sens.

Note that if you name the complement, it is normally introduced by de

C’est de la faute de ma mère.

but Grevisse says that

C’est de la faute à ma mère.

is more informal.