The four-time champions defeated Costa Rica 4-2 but were knocked out due to Japan's surprise 2-1 win over Spain, which saw the Blue Samurai top the group. Despite also finishing on four points, Spain progressed ahead of Germany on goal difference.
Havertz, who scored two second-half goals after coming off the bench on Thursday, said the way the players found out about their World Cup exit made it even more difficult.
"When it happens this way, it feels like watching like a horror movie," said Havertz. "We learned during the match that Japan were leading, and then the rankings were displayed in the stadium. We still had a little hope that Spain would score. But then we noticed that the Japan match was over".