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.