As a matter of fact, Russia did not “lose” any lands on the Eurasian continent in the 19th century. A side-by-side comparison of maps of the Russian Empire showing 19th and early 20th century borders would easily confirm this.

What the Russian Empire did do, however, was sell its overseas territories in North America to the US. The Russian Fort Ross settlement in California went to the US in 1842, while in 1867 Alaska was sold for a paltry $7.2 million (just over $100 million in today’s money).