They did have that sovereign power. The AoCs said they did:As a result of having ratified the Articles of Confederation and Perpetual Union, none of the individual States had the sovereign power or ability to "enter into any conference, agreement, alliance or treaty with any King, Prince or State". This would apply to
all the States except threethe first three listed here; the rest had not yet ratified; the last, Maryland, did not actually sign off on the Articles until 1781, but usually acted as if she had.
"Each state retains its sovereignty, freedom, and independence,..."
They had merely agreed, via a treaty, not to exercise a number of their sovereign powers on their own:
"Finally, several sovereign and independent states may unite themselves together by a perpetual confederacy, without ceasing to be, each individually, a perfect state. They will together constitute a federal republic: their joint deliberations will not impair the sovereignty of each member, though they may, in certain respects, put some restraint on the exercise of it, in virtue of voluntary engagements. A person does not cease to be free and independent, when he is obliged to fulfil engagements which he has voluntarily contracted." ─ Vattel, The Law of Nations
Keep in mind, sovereignty is a legal concept/designation. Having sovereignty (control over sovereign powers) doesn't need to have anything to do with actually exercising those powers. Under the Constitution, the people of the US delegated sovereign powers to the Fed, but retained the sovereignty (control) over those powers. Under the AoCs, the individual states delegated sovereign powers to the Confederation Congress, but retained the sovereignty (control) over those powers.
In addition, treaties do not have the force of law upon sovereign nations (otherwise, they would not be sovereign). This is 1) why the states could disregard the AoCs without any real consequence, and 2) why no treaty among the states (confederation) would work (as per G. Morris in the Const'l Convention), and why the AoCs (a treaty) had to replaced by a fundamental law (the Constitution). Sovereignty (control) over the sovereign powers exercised by the central government had to be removed from the respective states (the people of the individual states) and placed with the people of all the states. Both plans, AoCs and Constitution, prohibited the states from exercising certain sovereign powers. One worked and the other didn't, because the Constitution is a law (backed by sovereignty), and the AoCs were merely a treaty (voluntary agreement) among sovereign states. This difference is what makes the US under the Constitution a "more perfect Union." In addition, the Union was perpetual in both cases. But in the first case, its perpetuity was guaranteed by a treaty, which is no real guarantee at all, and in the second it was backed by the force of law (which only sovereignty can provide). The Framers and the people did not expend all that effort to draft and implement a completely new, unprecedented in world history system because it worked the same way as the AoCs/Confederation. These facts are also why secessionists expounded state compact theory. They were trying to turn the Constitution into just another treaty of confederation, which it clearly is not.