The Union Army dwindled back to peacetime levels within a few years of Appomattox and the means to enforce a more thorough reconstruction weren't really there, the army only really had a significant presence in urban areas and the terror was largely unchecked in the countryside.
But really it wasn't handled properly because the political will for it never existed. For most people in the North, racial equality was never an end in itself. For Democrats, of course (roughly 45% of Northerners) it was never an end at all. As for Republicans, their main concern was to stop the Southern states being governed by elements disloyal to the Union, who might raise another rebellion. However, it soon became evident that this wasn't a serious problem, that most ex-rebels were willing to accept the failure of secession, as long as they were left alone to run their states as they wished, especially where race relations was concerned. Once this was recognized, black rights became at best an irrelevance, at worst an obstacle to sectional reconciliation, so it didn't take too long for them to be abandoned. The Radical Republicans weren't going to exist forever, and the nation as a whole, despite disagreements on slavery, were pretty united in the idea that blacks were inferior. A longer military occupation was just going to make Southerners angrier without changing the end result. Eventually the North would have to withdraw and things would boil over. The tragic truth is that Reconstruction was doomed to failure.