Good question. There are a couple of factors to take into account. The first thing is that much of the Russian Civil War was fought by fairly small forces. According to PBS, Russia mobilized 12,000,000 soldiers during the First World War, lost 1,700,000 killed, 2,500,000 captured or MIA, and 4,950,000 wounded, a whopping casualty rate of 76.3%. Even acknowledging that some wounded would recover enough to fight again, that's a devastating count.

However, Russia's population was 166,000,000, in 1914, according to Spartacus Educational, so even given these devastating losses, there were still men of fighting age, including men involved in industry who had not been conscripted into the army. In fact, feeding Russia's population during the Civil War was a major problem, and more died from famine and disease than combat or political violence.

But you still certainly have a good point, and indeed the initial phase of the Russian Civil War was fought by small bands of soldiers and irregulars. Bruce Lockhart, a British diplomat sent to Moscow, estimated that the Bolshevik Army had 213,000 soldiers in 1918, split between those fighting the Whites in Siberia, in the Caucasus and Central Asia, and screening the German Army in the west.

Most of these were ill-disciplined worker's militias, deserters, Chinese laborers, and Austro-Hungarian (mostly Hungarian) POWs who joined out of conviction or to avoid starvation in abandoned prison camps. The backbone was formed from 23,000 committed Communist Lithuanian riflemen, who were rushed from front to front to deal with crises. So while there were still troops, the numbers were greatly reduced from the Russian Amy's wartime strength.

The Whites had even worse problems recruiting soldiers. General Denikin's Volunteer Army, the main White force in South Russia, set up recruiting offices in the Don, but only had around three thousand soldiers for most of the year, plus several thousands Don Cossacks. The vast majority of officers preferred not to get involved. The fact that the Volunteers often beat much larger Red forces is attributable to the fact that most of the them, even in the rank-and-file, were officers, and they were much better disciplined than their opponents. In North Russia, the British-backed government in Archangel never raised considerable numbers of troops (and those they did often deserted en masse), while the backbone of the Siberian Whites in 1918 was the 70,000-strong Czech Legion. So, we can see that only small numbers of men actually fought during the first phase of the war, on very vast fronts, and that the best fighters were not Russians, but foreign soldiers.

The war kicked up a notch in 1919, and both sides were forced to conscript soldiers. The Reds also conscripted former officers into the Red Army and coerced them to fight by holding their families as hostages. However the majority of the conscript soldiers on both sides were not very interesting in fighting, and tended to desert when it suited them. White armies converged Red Russia in 1919 from three sides, reaching their high-water mark in 1919, but the Reds possessed Russia's populous, industrial center, while the Whites were confined to the peripheries in the Baltic, Ukraine, and Siberia. Thus, the Reds could raise far more troops, and with the help of internal lines could focus on one threat at a time. While the Reds could replace losses, the Whites had a much harder time doing so. In Siberia, the Reds usually conscripted prisoners that they took, but the Whites shot theirs or stripped them and left them to freeze to death, rather than enlisting them. By the autumn of 1919 every major White threat had been defeated and the war was as good as over, but it continued for several more years.

So, I hope that answers your question. In short, the major points:

1.) Russia took huge losses in WWI, but still had a massive population.

2.) The war was fought by relatively small numbers of soldiers.

3.) Both sides did have trouble finding soldiers (especially willing ones), and resorted to conscription or enlisting prisoners by force.

Sources:

Richard Pipes, Russia Under the Bolshevik Regime

Mr. Lockhart to Mr. Balfour, "Memorandum on the Internal Situation in Russia", British Documents on Foreign Affairs, Doc. 5.

John Bradley, The Allied Intervention in Russia

Jonathan Smele, Civil War in Siberia: The Anti-Bolshevik Government of Admiral Kolchak