The place of the adverb is a somewhat fuzzy thing because it can vary a lot depending on what you want to say. It seems that you do not want to modify the infinitive faire but il suffit que.

I would say the most usual way to say it would be:

Il ne suffit (tout) simplement pas de le faire.

If you wrote:

Il ne suffit pas de le faire (tout) simplement.

could be ambiguous since, according to the more general context in which you use the sentence, it might be understood as modifying le faire, thus meaning “it’s not enough to do it in a simple manner”.

Note that you could have (de) le faire at the beginning of the sentence. It would give more importance to the words but would not change the meaning:

Le faire ne suffit (tout) simplement pas.*

Instead of simplement you could also use the adverb uniquement or the adverbial phrase rien … que.

Il ne suffit pas rien que de le faire.
Il ne suffit pas uniquement de le faire.
Uniquement le faire ne suffit pas.
Le faire uniquement ne suffit pas.

Some people would even use the adverb juste:

Il ne suffit pas juste de le faire.
Juste le faire ne suffit pas.

but a lot of (other) people consider that this use of juste is an anglicism.

*_{You don’t need the de in that case.}