See, e.g., the 1925 Ottoman public debt arbitration, the ILC draft articles on state succession, as well as an interesting article in the September 2011 edition of the Leiden Journal of International Law by Emre Otkem. Turkey remains responsible for the legal obligations, including the obligation to make reparation for legal wrongs like the Armenian genocide, that it's predecessor state incurred, insofar as those claims relate to the territory or people of the successor state. If you are willing to make the argument that a) Italy is a successor state to the Roman empire (quite a difficult historical argument to make), and b) the acts of the Roman legions were unlawful under international law of the time, then, yes, then we could talk about Italy. Both of those are true for the Ottoman empire/Turkey, but are not for Italy, thus the distinction.
U.S. says working on initiative to de-escalate Syria fighting, with focus on Aleppo (Reuters)
from the article: Turkey slams France over Armenian genocide bill