Please point out the many naval conflicts that the Soviet union has been in since the end of WW2 (having their own subs and ships sink due to engine faults does not count) as i'd be deeply interested to hear and read about them. And the Soviets are still on the short end of the technology stick and are VERY heavily outnumbered by navies that do a lot more training than they do at sea, mainly because Western Warships are in a running condition. Whilst the Soviets built a lot of ships, most of the ones in Russian service have been canibalised to keep the few runners they've got in working condition, they'd be in no fit state to bring them back to operating condition as well as getting enough trained crews for them in anything short of a decade of hard work and investment.
Soviet subs do not go to sea anywhere near as often as they use to in the cold war, their surface ships are mostly dockyard queens too. They've not introduced a new major surface ship since the Sovremenny and Udaloy classes of the 80's, and they have vastly cut back on their sub fleet so they only have Akula's and some old Victor III's left along with what ever operational Oscar II's they can get running. Also the USN for its faults (*glances at their current procurement plan*) is still very well trained and again has a considerable technological advantage over the Sovi..Russians. Then factor in I assume the RN which was and still IS NATO's main ASW force which is vastly experienced even if they make do with older kit for the most part, the Germans, Dutch etc, all of whom trained like bastards and still do in things like ASW.
Also looking here..
http://en.wikipedia.org/wiki/List_of_active_Russian_Navy_ships (yes I know not the best sauce but enough) you'll see that most of their most modern subs the Akula's are under refit leaving 24 year old Victor III's to carry the weight. Sorry this fleet could not overcome NATO and control the seas off Europe.