Belgium (15 points) failed to advance after finishing third in Group A. Germany were top on 30 while second-placed Turkey (17) booked a play-off spot following their 1-0 win over Azerbaijan.
Mesut Ozil and Andre Schuerrle struck late in the first half and Mario Gomez added another goal just after the restart, dashing Belgium's hopes of recording their first victory against Germany since 1954.
"I think it was important to push through at the finish line and show the Germans do not let up even if they have qualified," coach Joachim Low told reporters.
"That was also a message to other teams out there, that we do not stop."
Low left out Bayern Munich duo Bastian Schweinsteiger and Jerome Boateng after they picked up knocks in Friday's 3-1 win over Turkey and made four more changes to his starting line-up.
Fellaini's late consolation goal could not prevent Belgium losing to the Germans for the ninth consecutive time.
"The German team was too strong tonight," said Belgium coach Georges Leekens. "But you saw in the opening 20 minutes that little Belgium can also play football.
"I am proud of how my team played but we were missing some key players. Now our focus shifts to the 2014 World Cup."
