I realize that human capital is an important economic resource, and the Soviets lost far more of it than anyone else in the war. I was wondering if this had a significant impact on the post war soviet economy, and its ability to compete with the post war American economy considering the U.S. didn't lose nearly as many people.
No, not at all. At least, not in the sense you are talking about. Despite the immense devastation of World War Two, the Soviet Economy was reorganized, realigned, and rebuilt, to churn out industrial goods. Much of this came from Lend-Lease aid. But that aid didnt simply disappear after the war. The Soviet Economy continued to develop, and the country remained an industrial powerhouse up until the collapse in 1990.
But the massive casualties of the war had a massive psychological impact on the post-war population, and especially those in charge of the USSR. Those leaders were determined to prevent another repeat of 1941, regardless of who it alienated or what the risk.