It is true that this rebellion highlighted the need for a stronger central government. However, it is even more important to point out that the rebellion highlighted the need (in the minds of the elite) for less democracy. One of the major things that the rebellion suggested was that America was too democratic. The Constitution was written (in part) to mitigate the influence that the people could have on the government.
In the time leading up to Shays's Rebellion, states were passing all sorts of laws meant to help people (especially farmers) who were in debt. These laws were pretty radical at times (mandatory debt forgiveness, for example) and they scared the elite. These laws made it very difficult to build a good economy. Why, for example, would anyone lend money if the government might step in and say the money did not need to be paid back? Without lending, the economy dies.
The point is that democracy was making the government do stupid things. The people were asking the government for things that would ultimately hurt the country. Shays's Rebellion turned to violence when Massachusetts' government would not enact such laws. That really scared the elite--they saw the potential for the common people to turn to violence to get short-sighted and very harmful laws.
Because of this, the elite wrote the new Constitution. In it, power was moved away from the people. It was given to the central government. That government was run mostly by people (President, Senate at that time, Supreme Court) who were not directly elected by the voters. This shows that a major point of the Constitution was to reduce the amount of democracy and popular influence on the government.
Shays' Rebellion was a stunning reminder that gaining independence and freedom was vastly different than preserving it. The framers of the Articles were unaware of the challenges facing the new nation and the economic and political realities that confronted it were beyond calculation for them. The fight against the British for independence was a challenging element, but nothing as challenging as having to preserve the new Union. The nation's first constitution, the Articles of Confederation, reflected this challenging reality. On one hand, the Articles addressed one of the major fears of the framers of limiting central authority, ensuring that state autonomy was preserved at all costs. The reality that this caused was to create a situation where there was no authority to ensure that the nation, as a whole, could progress.
When Daniel Shays and his band of angry farmers took to protests, there was little national recourse for such an action because of the "loose confederation of states" nature of the Articles. In this light, Shays' Rebellion proved that some level of federal authority was needed to ensure that the problems that caused the rebellion could be addressed on an effective national domain and that the responses to such uprisings could be ones that represented the nation, working as a unified element. Shays' Rebellion demonstrated the need for a revision of the Articles into a more national form.