Manpower was not a key issue in the South's defeat. In fact, the outnumbered South was doing quite well for the first two years of the war, primarily due to superior military leadership and the equipment and weapons that were in-place prior to the secessions. Those weapons and that equipment eventually wore out, and replacements were hard to come by.
Of far more importance than headcount was the inability to support the war logistically or financially over the long-term. You had a major industrial power waging war against a rural, agrarian society.
Cotton and corn were no match for foundaries and factories.
That handwriting was on the wall long before 1861. Had the Southern States simply left the Union and left it at that, Lincoln would have been powerless to do anything about it...
...but all it took was one goober with a mullet and Trans Am, drunk on Busch Light and half deaf from listening to Lynyrd Skynyrd and .38 Special eight-tracks, to light a match, turn to his buddies in Charleston and say, "Hey, watch this...."
That gave Lincoln the excuse he needed!
Outnumbered?