That's a very Americentric view of abolition which completely ignores things like the work done by the West African Squadron. Do you really think abolitionists elsewhere are going to go 'well, I guess we might as well give up' because some slavers won a war?
For a view that the US victory over the Confederacy did indeed advance abolitionism internationally:
"The American Civil War was also a critical turning point in the struggle over slavery in both Cuba and Brazil. The defeat of the slaveholding Confederacy had a powerful effect on public opinion in both empires...The 'civilized world' had condemned slavery, and abolition in the United States was the last nail in the coffin of proslavery respectability. In Spain an abolitionist society formed in 1865, and Spanish legislators raised the question of the future of slavery in the Caribbean. In Brazil, Dom Pedro II suggested to his cabinet that they consider a plan for gradual emancipation; *all of these actors explicitly noted the end of slavery in the United States as a principal motivating factor.* [my emphasis--DT]
"With Washington DC no longer acting internationally in the interests of slaveholders, the United States finally cooperated with Great Britain in its decades-long effort to abolish the transatlantic slave trade. The Anglophone nations pressured Spain, which formally abolished its slave trade in 1866. The Spanish government also created the *Junta de Informacion sobre Ultramar* to consider colonial reforms, including the gradual abolition of slavery...The Junta disbanded with few accomplishments, which frustrated the ambitions of colonists and abolitionists alike and laid the seeds of a war on independence that would come.
"Spain's actions inspired Dom Pedro to finally make public his desire to see gradual abolition in Brazil. His 1867 address to the newly elected Chamber of Deputies charged them to consider the future of the empire's 'servile element' with a view to ending slavery. With small steps, the emperor had already begun to act toward this end. In July 1866 he responded to the petition of a French abolitionist society by observing that emancipation was 'nothing more than a question of method and opportunity. In November he granted freedom to government-owned slaves who agreed to serve as soldiers in the Paraguayan War and strongly encouraged private slaveholders to grant manumissions for the same purpose. But slaveholders were Dom Pedro's most powerful supporters, and their interests would not be ignored. These initial steps foundered, but the question of emancipation had been raised, and it did not go away...
"Conflict in Cuba and the Spanish government's [1870] Moret law contributed powerfully to Dom Pedro's ability to move the passage of Brazil's own [the Rio Branco Law]...Like the Emancipation Proclamation in the United States these laws were more important for their symbolic impacts than for the number of enslaved people freed through the formal mechanisms they put in place...
"In the urban centers of Brazil, which had grown in wealth and sophistication over the years, the advance of international abolitionism inspired many. Brazil's abolitionist movement took off in the late 1870's when reformer-legislators...became disenchanted with the inadequacy of the Rio Branco Law and publicly dedicated themselves to immediate abolition.."
Edward B. Rugemer, "Why Civil War? the Politics of Slavery in International Perspective, " in *The Civil War as Global Conflict: Transnational Meanings of the American Civil War* edited by David T. Gleeson and Simon Lewis (University of South Carolina Press 2014).
https://books.google.com/books?id=Ucy7BwAAQBAJ&pg=PT27
Also, on Brazil, see Gerald Horne,
The Deepest South: The United States, Brazil, and the African Slave Trade https://nyupress.org/books/9780814736883/ on the interest taken by southerners in the idea of an alliance of the world's two great slaveholding powers.,