Here's the exact quote, Hitler providing his rationale for the Final Solution began:

"Nature is cruel. Therefore, we too may be cruel. If I don't mind sending the pick of the German people into the hell of war without regret, then I have the right to destroy millions of men of inferior races who increase like vermin."

This is an unambiguous statement of Hitler's rationale. If a nation has the right to send its own soldiers to die in battle (without regret), why would a nation have compunctions about sending Jews to their deaths?

The ideology of warfare was the independent variable, genocide the dependent variable. 

 Koenigsberg