The Wehrmacht was busy. It was fighting for its life against the Red Army in the most consuming military campaign ever conducted. It was losing millions of men. Its supply lines were overextended. Its soldiers were freezing. The German army's relationship to the Jews of the East was not, primarily, one of genocidal intent. It was one of terrifying indifference because they had somewhere else to be.
As a Jew, this is a hard thing to say, and a harder thing to feel. You want your murderer to care enough to murder you. The reality is in some ways worse: the Wehrmacht rolled through these towns, sometimes confiscated supplies, occasionally issued anti-Jewish decrees or assisted the Einsatzgruppen (German mobile killing units), and then moved on to the real war. They left the Jews to the locals. And the locals were hungry.
He's saying the locals had lots of grievances against the Jews, not that they ate them like with fava beans and a nice Chianti.
There was a massive shortage of lampshades and soap in those areas