Mario Gotze's strike arrived with just seven minutes remaining in extra time, and Hummels believes that a slice of good fortune allowed the Germans to clinch their fourth title.
"I am still completely trapped in another world, physically too exhausted to be able to rejoice euphorically, but that will come in the coming days," the centre back told reporters.
"You can only be world champions when you act as a team. We wanted to make that clear to everyone the whole time and we achieved that, even if we got that little bit of luck in the final as we were already a bit waiting for penalties."
It is the first title for Germany since reunification in 1990.