Sir Alex Ferguson's side produced a subdued performance in which they started slowly and threw away their first-leg 3-2 advantage.
Throughout the entire 90 minutes they also never looked like breaching Milan's experienced rearguard.
Kaka tormented United in the first meeting at Old Trafford and the Brazil playmaker was again at the heart of all the home side's attacking moves as they roared out of the starting blocks.
Nemanja Vidic returned from the broken collarbone which had kept him sidelined since March, but in truth he struggled to cope with Kaka, who fired Milan into a deserved 11th minute lead.
Clarence Seedorf twisted his body to divert a long ball into the path of Kaka, who drilled a low shot into the bottom corner of the net with his left foot from the edge of the penalty area.
Ryan Giggs tested Dida with a low shot from 20 yards, but Milan went 2-0 ahead on the half-hour mark when the impressive Seedorf turned from provider to goalscorer.
Gabriel Heinze and Vidic combined to create the opening with some sloppy defensive display and, when the ball eventually came out to Seedorf on the edge of the penalty area, he rode the challenge of the Serbian defender and also Darren Fletcher before lashing a low volley beyond Edwin Van der Sar.
After the break, United continued in the same manner as they were sloppy in possession and nervous in defence.
Filippo Inzaghi and Kaka both had chances to kill off the tie, before Fletcher sliced United's best chance of the night wide after he was teed up by Wayne Rooney from 18 yards.
Ferguson sent on Louis Saha in a bid to open up the home defence, but Milan soaked up the pressure with the energetic Gennaro Gattuso dominant in midfield before they then launched a decisive counter-attack for the third goal.
Vidic and Wes Brown were caught too far up field in the 79th minute and substitute Alberto Gilardino strolled through the middle before picking his spot past Van der Sar.
With it, Milan killed off any hope of a second-half United comeback and set up a repeat of the 2005 final when they lost out to Liverpool in a dramatic tie settled on penalty kicks.