Much would depend on where and how he fell. If his unit was routed and quit the field and the enemy was in persuit he might well had not recieved a decent burial at all. In major battles the burial process sometimes took months. Contractors were hired and little effort was made to ID the remains. If he died of wounds in hospital or prison he likely received a decent burial although any attempt to mark his grave is long lost. If you can locate the battlefield I would start my search at the nearest church yard old enough to have been in operation in 1864. Often these old churchs served as hospitals as well. Good Luck!