The Emancipation Proclamation was a combination of what we might today call an executive order and an action pursuant to Lincoln's authority as commander in chief. Did the slave states immediately cease and desist? Of course not. And Lincoln, while he might have hoped his proclamation would be enough, certainly knew that was not likely. In order for this proclamation to be effectuated, a war had to be fought.
A Constitutional amendment was passed immediately after the Civil War, the Thirteenth Amendment, which prohibited slavery, and which also gave Congress the authority to pass laws to effectuate the amendment. Once we were no longer a nation at war, it was clear that the southern states would do everything they could to perpetuate slavery or at least would make life difficult or impossible for former slaves, and if we were no longer at war, a president would have no authority as commander in chief to enforce a proclamation. Hence, we needed to add to the Constitution to outlaw slavery and to give Congress the authority to pass laws to outlaw it and to enforce those laws. There was nothing in the original Constitution that gave Congress such authority. The series of amendments that followed were also designed to give Congress the ability to pass laws that would render illegal many of the subsequent actions taken by the southern states against the former slaves.