It was single most important operational factor
There are many causes and factors that would explain catastrophe befalling Soviet Union in summer of 1941, and subsequent defeats in 1942/early 1943. We could talk all day about purges in officer corps after Tukhachevsky affair, technological lag (especially considering radio), lower education level of Soviet peasantry (bulk of population), inhumanity and sycophancy of communist system, hatred or indifference of large parts of population toward said system etc ...
However, if we limit ourselves only to military matters, things that decide outcome of a battle in given place an time, then utter failure of VVS almost everywhere (except perhaps in and around Moscow, which would be explained) caused much of the early pain for Soviets. It is a well known fact that USSR started the war with certain numerical advantage in aircraft and armored vehicles. Although VVS based itself on mostly obsolete types like I-16, I-15, I-153, Tupolev SB plus some modern types with teething problems, it was almost incredulous how fast it disappeared over front lines - almost by the end of June 1941 ! In fact, Soviet soldiers rarely saw their own aircraft right until the end of that year. Indeed, many of them would die never having a chance to witness Soviet air power that was one of the cornerstones of Soviet propaganda before the war.
What happened next was almost predictable. Soviet tank formations in 1941 were poorly led, often attacking without reconnaissance, infantry or artillery support. They did consist mainly of relatively obsolete T-26, BT-5 and BT-7 tanks with some early T-34, KV-1 and KV-2. Often, they would run into German anti-tank screen that would decimate them. However, considering sheer numerical superiority, they would certainly inflict much larger damage to Germans hadn't Luftwaffe hanged almost always over their heads. Few examples of this happened during battle of Brody - in places where Soviet armor did manage to strike Germans, German loses were not insignificant. However, after destruction of VVS, Soviet armored formations were left unprotected and subject of decimating raids. What is maybe more important, Soviet railway system and supporting elements like fuel carrying trucks (which were already in short supply in Soviet Union) were also heavily bombed during daylight. Of course, other units (especially artillery) received their fair share of bombing - as a result already in July of 1941 most Soviet units were milling mobs of confused infantry armed only with light weapons.
Compare this with German aerial offensive against Moscow in late July 1941. Germans already has ample experience in destroying enemy capital cities. However, their first and largest raid did just moderate damage, losses were described as between 6-7 bombers, with subsequent raids being smaller and again with some losses. Reason for this was fairly good Moscow air defense (especially for Soviet standards) and large number of fighter units dedicated for defense of capital. When Germans did get in near the Moscow later that year, bad weather, constant attrition, and those same fighters prevented them from achieving total aerial superiority as usual. Operation Typhoon unexpectedly failed, first strategic German failure in entire war.
But note that as soon as Germans pulled away from Moscow in January-February 1942 near Rzhev and Vyazma, Luftwaffe again gained upper hand and acted as force multiplier. This pattern was repeating in 1942, one notable example was elimination of Kerch landing where German aviation practically smashed tightly packed Soviet troops. Overall, dedicated and almost unopposed bombing of Schwerpunkt during advance on Stalingrad and oil fields continued until late autumn. Stalingrad itself was bombed to a ruble, with tens of thousands civilians being killed. Soviet commander Chuikov ordered his troops to get close to the enemy and therefore deprive him of aerial and artillery support, but this was tactic that was only usable in the city. Elsewhere, Soviets had to gradually and painstakingly rebuild their aviation, wait for bad weather, and even for opportune moment when Germans moved some of their aviation units to Africa (to counter Operation Torch) . Only under such conditions they unleashed Operation Uranus and encircled German forces in Stalingrad. Note that even in such circumstances Germans managed to partially supply their troops trough airlift, thus prolonging the fighting and allowing other units to withdraw from Caucasus.
Finnaly, we should mention Kursk. Often regarded as turning point in the war, it was also turning point in aerial warfare. VVS again suffered large loses in this battle, but first time in the war Germans could not achieve neither supremacy nor superiority over battlefield, which coincided with failure of offensive. Luftwaffe did blunt subsequent Soviet offensives , for example during Operation Kutuzov, but could not completely stop them. Period of second half of 1943 and early 1944 could be described as balance of power in the air. VVS did loose more aircraft, but Germans were no longer bombing with impunity, thus they started their long retreat towards Germany.