In hindsight, that's directionally correct even though it was not that obvious back then. Only freaks mentioned the nukes in the 90s for example. Now it's crystal clear that their stockpile alone should have justified much higher engagement from the first world. Possibly all the way to literally buying most of it. All kinds of things were possible in the early 90s.
We can definitely blame the US for forcing Ukraine to relinquish its nukes. We can blame the US for insisting for a long time on preserving the USSR (during the Gorbachev era). We can blame the US for not paying enough attention to the other two Slavic former republics early. We can blame America for not penalizing Yeltsin's regime when they started to veer off the original course.
But we need to remember that it was the West in general, not just the US. The EU is equally to blame. And even though the last 20 years are a direct result of the 90s not that much was done in those 20 years either. Not in 2008, not in 2014, not even when President Trump told the Germans to cut the pipelines and spend on the military.
It very well could be the case that destroying the Evil Empire was an unprecedented affair which was too hard for anybody. Where by hard I mean impossible in the Velvet Revolution style. Or at all. They had to perform multiple simultaneous transitions (Totalitarianism -> Democracy, central planning -> market economy, empire -> nation state). With a population impoverished by 70 years of Communism and three generations not knowing any other life (not the case in the Eastern Europe).
It's poetically fitting that Mr Gorbachev died the same year his entire legacy was erased. He was not perfect, he was an idealist, but he gave freedom to the people. It was him who opened the border and let millions escape.