Andrea Pirlo put the seven-times European champions ahead at the San Siro with a penalty in the 27th minute after Torsten Frings had blocked a David Beckham free kick with his arm.
Brazilian forward Alexandre Pato doubled the lead six minutes later, rifling the ball under the bar from outside the area at the end of a superb run from just beyond halfway to put Milan 3-1 ahead on aggregate.
The Germans, who were well on top before the opening goal and wasted good chances after Pato struck, hit back in the 68th minute when Pizarro nodded in a Diego free kick.
The Peruvian used his head again to dispatch a cross from the left 12 minutes from time and send Werder through.
The early exit will increase speculation that coach Carlo Ancelotti is in danger of losing his job, with Milan's Serie A title hopes looking slender as they trail leaders Inter by 11 points.
"They outplayed us in the first half, when we were fresher, and in the second," Ancelotti told reporters.
"It was continual suffering. We have to accept the way things went this evening and not be afraid to say Werder clearly deserved it. It's a delicate moment, we have lots of players injured.
"Anyway we are not a team in bits. We have to recover and not get depressed in order to hit the target of qualifying for the Champions League (next year)."
Italy full back Gianluca Zambrotta called on his team mates to get behind the boss.
"At the moment we have to be close to the coach and stay united to overcome this negative phase of the season together," 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."
VILLA & SPURS OUT
Former UEFA Cup winners CSKA Moscow took full advantage of an under-strength Aston Villa team by easing into the last 16 with a 3-1 aggregate win.
Villa manager Martin O'Neill had made no secret that his season's goal was securing a Champions League qualification place in the Premier League and fielded just three of the starting side that lost 1-0 to Chelsea last weekend.
A 1-1 draw in the first leg at Villa Park left all to play for but in sub-zero temperatures in the Russian capital, the 2005 winners proved too strong in a 2-0 win.
Yuri Zhirkov scored from outside the penalty area just past the hour mark and the competition's leading scorer Vagner Love took his tally to 10 with a crisp finish in stoppage time.
CSKA will play Shakhtar Donetsk in the second knockout round after the Ukranians scored a late equaliser at White Hart Lane to secure a 1-1 draw on the night and 3-1 win on aggregate. Giovani netted for the Londoners.
