Ah the Black Army. What romantics! What dreamers! What fools!

The Black Army (and their forebearers the Black Guards-- essentially the anarchist version of the communist Red Guards) were an anarchist movement in the Ukraine that represented the most organized and successful wing of the anarcho-revolutionary clique during the Russian Revolution. Their stated end-goal post-revolution was a free and independent non-state in the southern region of the former Russian Empire.

The tricky thing about answering this question, is that the outward Soviet perception of the anarchists significantly changed during the revolution as the Soviet position became more and more stable. I say outward here because I suspect that the Bolsheviks recognized the anarchist movement for the threat to their power it was from the moment people like Makhno began to garner significant attention, but just as they cooperated with the Mensheviks and Socialist Revolutionaries to a certain extent before ruthlessly purging their ranks, so too did Lenin, Trotsky, and others entertain fraternal relations with the nascent anarchist movement at the outset of the revolution and civil war only to stab them in the back, denounce them, and then murder a good deal of them as soon as doing so became feasible.

Based on the wording of your question, it sounds like you're after the bottom line though, which is this: the Makhno movement was crushed (quite literally) the moment the Bolsheviks were sure they no longer required their material support in order to win the civil war. The Black Army were portrayed as traitors and counterrevolutionaries in the Soviet collective memory henceforth.

Lev Trotsky's The Makhno Movement (1919) summarizes Bolshevik opposition to the Black Army quite concisely:

Makhno and his closest co-thinkers consider themselves Anarchists, and on this basis they 'reject' state power. So then, are they the enemies of the Soviet power? Obviously, since Soviet power is the state power of the workers and working peasants.^([)^(1)^(])

(Emphasis in the original)

Before 1920, during which Admiral Aleksandr Kolchak-- the internationally recognized head-of-state of Russia-- was captured and executed by the Bolsheviks and the slow crush of inevitable defeat pressed down upon the White Army, when Soviet rule over the country was still far from a certainty, the latter were far more accommodating to the anarchists (who theoretically resisted Lenin's centralized Soviet power structure), but as Bolshevik victory grew more and more inevitable, this erstwhile friendliness was eroded further and further and the anarchists in general (as well as Nestor Makhno and his Black Army specifically) were presented more and more as counterrevolutionaries.

What does that mean?

That means that on one hand you have Vladimir Lenin referring to 'the most dedicated supporters of Soviet power,' in reference to the anarchists and on the other hand 'Soviet newspapers [...] attack[ing] them as 'kulaks' and 'Anarcho-Bandits.''^([)^(2)^(]) The bulk of the anarchist movement supported Bolshevik power as the lesser of two evils in the Russian Civil War in the hopes of working towards statelessness after the war was won.

This attitude is personified by Russian emigre-turned-immigrant Bill Shatov (meaning he left Russia for the United States in 1907 and returned in 1917 when the revolution occurred), who said of Bolshevik-anarchist cooperation:

We anarchists should remain true to our ideals, but we should not criticize at this time. We must work and help to build.

And is reinforced by the anarchist-terrorist-turned-Bolshevik Yuda Roshchin (Sometimes transliterated Judah Grossman):

It is the duty of every anarchist to work whole-heartedly with the Communists, who are the advance guard of the Revolution. Leave your theories alone, and do practical work for the reconstruction of Russia. The need is great, and the Bolsheviks welcome you.

You can see hints of the iron fist to come in Trotsky's contemporaneous writings but the sad irony is that many of the standard operating protocols of the Black Army were actually quite similar to the initial operating protocols of the Red Army (see this answer I wrote about military support for the Bolsheviks after Order No. 1 of the Petrograd Soviet which sought to 'democratize' the army).

From Trotsky:

Makhno's 'army' is guerrilla-ism at its worst. [...] No hint of order and discipline is to be found in this 'army.' There is no supply organisation. Food, uniforms and ammunition are seized wherever they happen to come to hand, and they are expended in the same careless way. This 'army' also fights when it feels like it. It obeys no orders. Individual groups advance when they can, that is, when they encounter no serious resistance. [...] The blame for all this lies wholly with the muddle-headed and dissipated Anarchist commanders.

In this 'army,' commanders are elected [...] the Makhnovite commanders reflect the interests of a minute group of Anarchists who rely on the kulaks and the ignorant.

Electing officers (or more specifically, extra-military committees who could appoint officers) was item number one of the aforementioned Order No. 1 showing just how quickly the Bolsheviks had completely amended their ideology during three years of horrific, internecine civil war:

In all companies, battalions, regiments, batteries, squadrons and separate services of various military departments and on board naval ships committees shall be immediately elected from among representatives of the rankers of the foregoing units. ^([)^(3)^(])

In late 1919 and early 1920 the Red Army chain of command, at the head of which was Lev Trotsky remember, issued orders to Makhno and his Black Army to press towards the Polish Front and aid Mikhail Tukhachevsky's efforts there in the Soviet-Polish War. Makhno rightly recognized this order as an attempt to force the Black Army to evacuate their own territory and create a vacuum which Trotsky and his Red Army could move in and fill should they obey, or demonstrate direct insubordination and expose themselves to Bolshevik propaganda decrying their non-cooperation and lack of collective efforts should they refuse.

Makhno refused and Trotsky sent the Red Army to the Ukraine to destroy them. After about eight months of conflict that saw typhus ravage the Black Army (who was already severely outnumbered and relied almost exclusively on guerrilla tactics), the Bolsheviks once more extended an olive branch-- welcoming Makhno back into the fold of Bolshevik power and blanket amnesty for all imprisoned anarchists should they aid with the upcoming offensive thrust to the Crimean peninsula. Makhno accepted this offer only to be betrayed less than a month later after the Black Army aided the Red Army in the 1920 defeat of Baron Wrangal in Crimea. Immediately upon Wrangel's defeat, Black Army leaders present at the battle were rounded up and shot. The next day, Makhno's operating headquarters were raided, more leaders were shot, and Trotsky resumed his antagonistic rhetoric towards the anarchists.

Is it thinkable in such a situation to permit on the territory of the Soviet republic the existence of armed bands which form themselves around atamans and Batkos, bands which do not recognise the will of the working class, which seize whatever they like and fight with whomsoever they choose? No, it is time to finish with this Anarcho-kulak debauchery, to finish with it firmly, once and for all, so that nobody will ever want to indulge in such conduct again.

Makhno himself escaped the Ukraine and lived out his life in exile in Paris where he continued writing and decrying the Bolsheviks (thereby helping to cement his own denunciation within the USSR).

From Makhno's Soviet Power-- Its Present and Its Future (1931):

The lunacy of this regime must be eliminated and replaced by the vital principles of the exploited workers, on a basis of solidarity, freedom and equal voice for each and every person, in short, for all concerned with genuine emancipation. ^([)^(4)^(])