According to the linked Wiki article:
The disappearance of the lake was no surprise to the Soviets; they expected it to happen long before. As early as 1964, Aleksandr Asarin at the Hydroproject Institute pointed out that the lake was doomed, explaining, "It was part of the five-year plans, approved by the council of ministers and the Politburo. Nobody on a lower level would dare to say a word contradicting those plans, even if it was the fate of the Aral Sea."
So the plan from the beginning was to have the Aral Sea disappear.
Some Soviet experts apparently considered the Aral to be "nature's error", and a Soviet engineer said in 1968, "it is obvious to everyone that the evaporation of the Aral Sea is inevitable."
In fact, it seems that "some" Soviets considered the Aral Sea an "error" to be corrected.
From 1960 to 1998, the sea's surface area shrank by about 60%, and its volume by 80%. In 1960, the Aral Sea had been the world's fourth-largest lake, with an area around 68,000 km2 (26,000 sq mi) and a volume of 1,100 km3 (260 cu mi); by 1998, it had dropped to 28,687 km2 (11,076 sq mi) and eighth largest. Over the same time period, its salinity increased from about 10 g/l to about 45 g/l.
In 1987, the continuing shrinkage split the lake into two separate bodies of water, the North Aral Sea (the Lesser Sea, or Small Aral Sea) and the South Aral Sea (the Greater Sea, or Large Aral Sea).
So, by the time of the collapse of the Soviet Union, 80% of the lake was gone and had already split into several smaller lakes.
So, yeah, I think we can blame the Soviets. That it is now hard to reverse the facts on the ground is to be expected.