Ancelotti said: "Inter, at least to begin with, had a much more prudent approach. This favoured us because we had the chance to build our play and more freedom for Alessandro Nesta and Massimo Ambrosini.
"I think this year we paid a heavy price for injuries to people like Inzaghi, Kaka, Ronaldo and Pato. Let us not forget Pippo was sidelined for three months.
"You can really tell the difference when he is in good physical shape and he knows that too. At the moment he is in a brilliant period of form and this allows us to have many different options in attack."
Kaka set up the opener and scored the second goal himself to end a run of three consecutive derby defeats.
"We were missing the feeling of a derby victory," smiled the Brazilian. "Today everything went well. They could have won the Scudetto, but they didn't, and on top of that we recaptured fourth place. Now it all depends on us.
"We did what Inter should have done today. However, it does increase the regrets for the games we did not win at San Siro this season."
Inter coach Roberto Mancini insisted there was no need to panic after seeing their lead cut to just three points.
He said: "The big party will happen when we win. I always thought it would be next Sunday against Siena.
"In the first half Milan did well, but the game was under control. After conceding the second goal we started to really play and would have deserved a draw."