This is an incredible question and I'm very glad you asked. Before I answer it, I'd like to briefly describe what Shay's Rebellion actually was:

Context:

Shays' Rebellion was an armed uprising led by former Massachusetts Militiamen and Veterans of the American Revolution which took place between 1786 - 1787. Daniel Shays led several thousand "rebels" to fight against the economic injustices that were facing farmers and agrarian peasants all across America. These farmers were experiencing extreme poverty following the end of the Revolutionary War. All across Massachusetts (and the rest of America) farmers saw their lands foreclosed on in unfair property seizers, and they wanted to fight back, which they did here. They were also trying to fight taxes which were beginning to be levied against them. They fought this in many ways, but among them was closing and obscuring roads so that government agents couldn't reach rural parts of the state. Shays' Rebellion would ultimately be put down, but it startled the gentry who feared further uprisings throughout the United States.

I also like to point out that the naming of this event is really interesting. The people who did this, called themselves Regulators ( modeling off of the North Carolina Regulators who also fought against economic injustices before the start of the American Revolution.). The idea of Civilian Regulation was a popular idea that sought to end government corruption and stamp out the overwhelming power of the gentry. They believed that if the government wasn't regulating itself on behalf of "We the People", then "the People" had the right to regulate, or take back the government -- to take it back and do what they believed was right. They didn't see themselves as a rebellion, but rather the gentry labeled them as such in order to de-legitimize their cause. The gentry didn't want to call these men "militiamen" or "regulators" for this reason (which they clearly were), but instead, branded them as "rebels" who needed to be stopped.

Veterans like Benjamin Lincoln would raise militias on their own and mounted their own assaults against the "rebels." They call themselves the "the Massachusetts Militia" even though it was the former militias who they were fighting! So as they begin to debate this on the national stage, especially in 1787 at the Constitutional convention, the gentry singled out Daniel Shay (even though there were actually many other leaders), and they said he was crazy and people were only following a demagogue. They hailed The Massachusetts Militia as the victors and saviors and asserted that militias are what will save America in the future against such madness.

Answer:

Although the Constitution is drawn up in 1787, it is not ratified until December of 1791 when the Bill of Rights was finally agreed upon. Whether or not to include the Bill of Rights (and what to include inside it) was a matter of extreme contestation between the Founders and everything within it was deeply fought over.

When we look at the Second Amendment specifically, we should look at a few things before hand. First, by the 1790s, other small rebellions had popped up all over the country. Terry Bouton's article "A Road Closed: Rural Insurgency in Post-Independence Pennsylvania" (The Journal of American History, Vol. 87, No. 3 (Dec., 2000), pp. 855-887) masterfully explains the fighting and rebellion that took place in the rural countrysides of Pennsylvania that mirrored what had happened in Massachusetts with Shays' Rebellion. Simply put, the gentry were terrified that they were losing control of rural America, and as a result they would not be able to seize foreclosed land and collect taxes, which they deeply wanted. Empowering militias to be trained and carry firearms allowed the gentry to call up these men in times of need and suppress these rebellions that were taking place.

Now there was already precedent in existence for protecting militias and their rights to bear arms in many states. Multiple other bills of rights from other states had already protected a militia's right to bear arms (such as Section 13 of Virginia's Declaration of Rights) and many of these states were fighting to have the federal government protect this as well.

Now, look at the very wording of the Second Amendment.

A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

"A well regulated Militia" is the key phrase. They are referring to the militias led by people like Benjamin Lincoln and his Massachusetts Militia not Shays and his "rebellion". The initial goal was to protect a state's right to call up arms against rebels, not to arm the masses. The Founders feared that in some states (like Rhode Island) that were already being drastically controlled by the poor (rather than the gentry), that local governments would start being able to choose who could keep and bear arms, and that by creating the Second Amendment, the gentry would always have the ability to call up and arm militias in times of need.

Clarification: I also need to stress that this question mentioned Jefferson by name, however he was not a signer of the Constitution, but did certify the adoption of the Bill of Rights in 1792.

Tl;Dr: The second ammendement wasn't passed in spite of Shays' Rebellion, rather it was passed because of Shays' Rebellion.

Edit: spelling