Russia has seen quite a few naval ships sunk or damaged to the point of tying up dry docks and repair facilities. The Russian navy has also been forced to move several of its major vessels from Sevastopol in Crimea farther from Ukraine, to Novorossiysk.
As for the US "taking advantage" of this, what does that mean? The Black Sea is landlocked, with one narrow entrance between European and mainland Turkey. Russian naval vessels in the Black Sea are almost trapped there, exiting with Turkey's knowledge and permission, and currently not allowed to enter (from the Baltic, Arctic, or Pacific Fleets) by treaty with Turkey (due to the war with Ukraine). The US maintains surveillance over the Black Sea using various types of recon assets.