Because they were bottlers (as a unit).
Plus Milan in the CL always held the upper hand because of their CL mentality and such forth. Betting on Milan in 2003 CL final was the safest bet I ever placed.
If Milan had the fortitude to turn up every week and not once every couple of weeks like in the CL then Juventus wouldn't have won so many Serie A titles either.
Milan imo had the Nesta and Maldini in defence, the best midfield in europe at that time (Gattuso, Pirlo, Seedorf, Kaka plus the likes of Rui Costa etc) and they had Inzaghi and Shevchenko up front.
Thus as seen from their CL seasons from 02/03 - 06/07 they were a much more complete team than Juventus but because their priority was always CL over Serie A at that time those players played to their maxim more in the CL than in Serie A.