While the Soviet Union lost 20 million casualties during the war, it should be remembered that (a) the majority of civilian casualties occurred in non-Russian districts, that (b) the Soviet Union at 180 million was the world's 3rd largest nation that could, to a callous observer, absorb the costs, (c) only half of that 20 million were young men; the rest were civilians of varying ages, (d) occupation of Germany and industrialization during the war boosted Soviet industrial production to the point where mechanized agriculture, if imperfect, finally sufficed to make famines a thing of the past.

The war was a brutal thing, but it was the mindset of the leadership postwar, the limitations inherent in authoritarian socialism, as well as the widespread realization of high Western living standards that sapped the Soviet Union of its faith in itself, its system and its money.

Indirectly though, WWII hobbled the Soviet Union. The war made Russia incredibly paranoid and fearful of invasion. Their army demobilized; their spending did not. Massive government spending to the military shuttled resources away from productive commercial enterprises, distracted the leadership from the needs of their people, and eventually pushed the nation to the brink. <Soviet Experiment, Suny>

TL;DR the fall of the Soviet Union came 45 years after the Great Patriotic War. It is unlikely that a hobbling economy would enter its highest productivity during the 1950s-60s.