Marco Borriello struck the only of the game at the San Siro.
"This result means a lot in the home of the League leaders," Ranieri said of the 1-0 win over Milan that puts them within seven points of the top spot.
"It was certainly not easy and winning here keeps us alive in the Scudetto race, albeit still aware of the difficulties. We felt the support of the fans and gave them a great Christmas present."
"Do I feel this is my victory? No. I am paid to make decisions and take responsibility when things go wrong. It went well today and I think it's right to praise the players.
"In the first half Alexander Doni and the defence managed to safe-guard the clean sheet, especially in that one-on-one with Zlatan Ibrahimovic.
"The team was very united and we knew how to suffer under pressure, then emerge in the long run. It's a sign all the work we're doing every day pays off."