Not all of them. In fact, not even most of them. Many remained in the German government a long time, simply because there was no one else.

This was what "denazification" ended up being all about: not so much filtering out the Nazis as seeing how many they could afford to filter back in. A film that gives a good sense of this is Von Trier's EUROPA.

(PS btw I cannot recommend EUROPA highly enough, it is a very good and very cleverly made film)