It was the third time in a row that two-time winner Juventus had lost in the final and, for Lippi, who was in charge each time, it hurt even more.
"It's really bad, it went bad, then with the injuries, everything went wrong, the whole evening went wrong," he said. "It's terribly bad, we are disappointed.
"We are not losers in the national championship but, in the Champions League, I don't know if we are. We have won so many exceptional matches, I don't think we can be considered losers."
Midfielder Gianluca Zambrotta said it was hard to watch his teammates miss penalties.
"When you lose after penalty kicks, it hurts a lot," he said. "For some of our team it was the third loss in a Champions Cup final, so it was additionally bitter. We trained penalties before the final, but emotion plays a big role at the end of the match."
Milan created the better chances in the first all-Italian final in the 48-year history of the competition and, although Shevchenko had a goal disallowed and Buffon made a stunning save from Filippo Inzaghi, Juventus held on to force extra time before 63,000 fans at Old Trafford.
Italian champion for the last two seasons, Juventus faced Milan without influentual Czech midfielder Pavel Nedved, who was suspended having collected three yellow cards in the competition.
Without his runs and all-round midfield energy, Juventus lacked midfield urgency and Milan had three good scoring chances in the first 45 minutes.
Few chances were created in the extra 30 minutes although Del Piero should have done better with four minutes.
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