I'm not quite sure how to answer this. The Southern States that seceded could not just stay an independent country because they lost the war. The war was literally fought over their ability to choose to stay in the Union or not. The options, like was said in the other comment to this thread, was to continue fighting (and losing convincingly) or reintegrating back into the Union.

If you want some easy reading on the leadup to the Civil War for about $4 on Amazon, check out The Impending Crisis, 1848-1861 by David Potter. I've personally not read it, but the wiki recommends Battle Cry of Freedom: The Civil War Era by James McPherson as an overall study of the Civil War, pre and post. Also used for about $5-10 on Amazon. I can't link it directly because AH blocks amazon links but just copy paste what I typed out and it's first result. I'd personally start with the latter as it seems more comprehensive.

Because those seceding lost. Their options were to either continue the war or come back and they chose to surrender and return.