The side from the capital beat the league leaders at the San Siro thanks to a goal from former Milan player Marco Borriello.
Menez set up the goal, and said afterwards: “Before the holiday this is a very important victory. I feel the confidence most of all, we can do so much more, and also aim for the Scudetto.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.