The "loss" of human capital was indeed a significant financial issue for many Southerners, but I'm not sure there was significant financial hardship inflicted on most Southern ex-slaveholders, given the way the Civil War and Reconstruction itself played out. Someone can feel free to correct me on this if necessary.

First, the South of 1860 was already dead by the end of the war, economically speaking. The war wrought extreme devastation on the South, financially and economically speaking, both from the battles themselves and from Confederate policies. That being said, even the prewar South operated on a barter system fairly regularly (not that there wasn't a currency value being assigned to transactions, it's just that actual currency was not always being itself exchanged).

Following the war, there was not a major shift in the economic structure of the South, apart from blacks no longer being considered legal property of course. By this I mean there was no lasting or significant land distribution, and most whites who owned land before the war still owned that land after the war. This gave them economic power, including over freedmen, which could be hauntingly similar to prewar relations. Almost immediately after the war, white Southerners sought (and in many ways succeeded) to restore as much of the prewar status quo as possible. Through the rise of sharecropping (or the crop-lien system), where a tenant farmer works a plot of land in exchange for food, housing, and farming implements (tools, livestock, etc) and a portion of the crop produced, let's say a quarter or a third. The rest goes back to the owner. This system doesn't necessarily require a lot of actual exchanges in currency and was often itself a debt trap that ensnared countless freedmen (and many poor whites, it should be noted) into essentially being beholden to an owner, sometimes indefinitely. That's a basic rundown of the system but it could very often resemble slavery in practice. I'm no economic historian (and would love to hear from one), but given this system I am not certain that the loss of "capital" that came from emancipation was as damaging in practice as it sounds on paper.

Regarding the compensation issue, I dare say that by the time the Emancipation Proclamation was out, the war was ending, and the 13th Amendment was in the works, that ship had sailed. Lincoln had been a strong advocate of compensated emancipation efforts (as well as colonization, the practice of trying to ship African Americans out of the country to Africa or the Caribbean) even well into the war. Prior to the Emancipation Proclamation, he attempted to convince the Border States to adopt such measures in their state legislatures (he felt that such change needed to be at the state, not the federal level) and was repeatedly rebuffed. Even little Delaware, whose population was only 1-2% slaves and was by far the least reliant on the institution, refused.

By the latter half of the war (after the Proclamation), the idea of compensated emancipation was discredited by the majority of the government and the North. To quote an example, Lincoln floated the idea once again as late as February 1865 in a cabinet meeting but dropped it after he was met with unanimous opposition. Gideon Welles, Secretary of the Navy, remarked that while peace with the South should be pursued, "there may be such a thing as overdoing."

Some Southerners did push for compensation after the war, Kentucky especially (being a Union state with slavery, though it had rejected compensation schemes just a couple years earlier). But frankly many Northerners were angry at the South for the war, for attempting disunion, and in some cases for slavery more directly. Many pushed for much stricter consequences for the South than actually occurred (largely because both Lincoln and later Johnson refused to exact them). Frankly, the idea that the South could start a very bloody war to break up the Union, in order to protect a widely reviled institution (in Northern eyes), lose, and then ask for monetary compensation for their losses from the federal government they just tried to declare illegitimate, would have been ridiculous.

Source for a bunch of this: Eric Foner. Reconstruction: America's Unfinished Revolution (page 74 for the quote)