Milan looked to be in command, holding an away goal from its 1-1 tie at Bremen and leading on goals by Andrea Pirlo (penalty kick after Beckham's free kick was touched by Torsten Frings with his arm in the box) and Alexandre Pato after a little more than a half an hour.
After that, Bremen dominated Milan in the air and had several chances before Pizarro scored in the 68th and 78th minutes.
Milan has been eliminated from the Coppa Italia and trails Inter Milan by 11 points in the Serie A title race. The latest setback intensified the pressure on Coach Carlo Ancelotti.
"At the moment, we have to be close to the coach and stay united to overcome this negative phase of the season together," Milan defender Gianluca Zambrotta said. "We are all disappointed about the failure to qualify, but we tried in every way to go through to the next round. Now we must look ahead and not give up because the [domestic] championship is not over, there are still lots of games to go and one of our aims is to conquer one of the top three positions."