Ludovic Giuly and Mirko Vucinic overturned Kaka's goal in three minutes for Roma's victory and Ancelotti moaned: "There is a great deal of regret over this loss. At times there are deserved defeats, others less so.
"The Giallorossi made the most of our late distractions and won a game where the right result would have been a draw or even something more for us.
"We played very well and unfortunately have dropped points. In all honesty, I didn't expect us to do so well tonight, as we were in control, took the lead and tried to extend our advantage."
He added: "I really cannot complain about the standard of football, but we still lost. Never mind, that is football. We must continue to play with this same quality and hunger, then I think we can achieve our objectives."
Roma coach Luciano Spalletti remarked: "There were moments in which Milan had the game in the palm of their hand and could easily have finished us off after they went ahead.
"My players did well to keep believing and push for the victory. Often if you take the right approach, you reap the rewards.
"Milan played extremely well and if they had won we could not have had any complaints. We could have done better on their goal, though, as we were a little disorganised."