Milan played a very good game.
They controlled the game and created two or three clear chances and had heaps of other balls played into a good area.
Ranieri got his tactics wrong. Roma should have played a higher lined, because Milan didn't have the pace to threaten in behind. Holding a higher line would also have allowed Roma to reduce the space in midfield and make it easier for them to close down Pirlo and Ronaldinho.
However, if Ranieri wanted to play that deep a line, he should have played Menez so that Roma might at least have posed a threat on the counter attack.