A costly mistake from Roy Carroll handed AC Milan the advantage in their tie with a narrow win at Old Trafford.
Carroll spilled Clarence Seedorf's strike late in the game and Hernan Crespo converted from short range.
Seedorf grazed the United bar in the first half, while Paul Scholes missed from 12 yards and Quinton Fortune hooked the ball just wide.
Ruud van Nistelrooy made his return from injury as a substitute and almost equalised with a header late on.
The visiting team improved as the match wore on and United took on a ragged and desperate appearance as they searched for an equaliser after Crespo's goal.
Milan coach Carlo Ancelotti had signalled his intentions by naming two playmakers - Kaka and Rui Costa - in his starting line-up to support lone forward Crespo.
And his team moved the ball through midfield with a precision and superb economy of movement that, at times, had United chasing shadows.
The visitors came within a whisker of scoring after just eight minutes with Seedorf's vicious free-kick.
But although United found themselves penned in their own half for long periods they held their shape for most of the game in an attempt to prevent Milan from playing balls into the space between defence and midfield.
And United, with Cristiano Ronaldo and Ryan Giggs looking to support Wayne Rooney, looked to break with pace.
A superb run from Fortune - cutting in from the left and breezing past Alessandro Nesta - created an opportunity from which Scholes should have scored.
But the midfielder, unmarked 12 yards from goal, uncharacteristically snatched at his shot and missed the target.
Fortune himself came within inches of scoring eight minutes before the break, hooking the ball past Dida but just wide of the post after a lightning break from Ronaldo had caught Milan short at the back.
The pace of the match intensified after the break, with Milan's superior passing stretching the United defence, while the home team squandered possession too easily in the middle of the park.
Sir Alex Ferguson introduced Van Nistelrooy for his first appearance since 27 November in an effort to wrestle the initiative back from Milan.
But still it was Milan who seemed more incisive and Wes Brown had to make a good block to thwart Crespo.
The Argentine had a further chance to score after collecting a superb pass from Kaka but he smashed his shot over the crossbar.
But he finally found his way on to the scoresheet with a simple tap-in after Carroll's error.
Kaka might have made it worse for United but he drilled a shot wide close to full-time, while Van Nistelrooy might have salvaged a draw but could not keep his header on target after a good cross from Gabriel Heinze.
Man Utd: Carroll, Gary Neville (Silvestre 80), Ferdinand, Brown, Heinze, Ronaldo (van Nistelrooy 62), Scholes, Keane, Fortune (Saha 80), Giggs, Rooney. Subs Not Used: Howard, Phil Neville, Smith, O'Shea.
AC Milan: Dida, Cafu (Costacurta 86), Nesta, Maldini, Kaladze, Gattuso, Pirlo (Ambrosini 84), Seedorf, Rui Costa, Kaka (Serginho 90), Crespo. Subs Not Used: Abbiati, Tomasson, Dhorasoo. Booked: Nesta.
Goals: Crespo 78.
Ref: Manuel Enrique Mejuto Gonzalez (Spain).