Short Answer: The Canadiens were tired of war and content with British rule.
Twenty-some years before the American Revolution (1754), which was just before the Seven Years War, this is what the map of British Colonies looked like:
Only a few areas of modern-day Canada were British then: Nova-Scotia, Labrador-Newfoundland, and around James' Bay & Hudson's Bay. Quebec extended south to below Niagara falls.
The 13 American Colonies were centered around New-York City:
1.) Geographic Separation caused the English speaking British colonies north of Maine to be culturally distinct from the 13 American Colonies. The people of Nova Scotia were half New Englanders and half Germans, Highlanders, Ulstermen and Yorkshiremen. Nova Scotia wished to remain neutral. British Naval power and a British Garrison at Halifax prevented any serious American attempt at invasion. In 1777 Nova-Scotian outposts came under attack from New England privateers seeking plunder. That caused even former New-Englanders to form militias and defend their homes. Soon thereafter the New Light religious movement (Great Awakening) started by Henry Alline of Rhode Island swept through New England and Nova Scotia turning attention away from Politics.
2.) Acceptance of British Rule: When New France fell in 1760, the defeated armies, French officials, some seigneurs, and some merchants returned to France. British credit, currency, and markets such as London was what mattered--not Paris or America. The British successfully implemented representative government in Quebec through respecting the religious freedoms of Catholics and recognizing the political value of the Catholic Church, which was backed by a dutiful French populace that contrasted sharply with the restive 13 American colonies.
3.) The Quebec Act of 1774 satisfied Quebec and angered the American colonies. It allowed English criminal law to exist in parallel with French civil law and the entrenched seigneurial system. Quebec even had a (legal) mandatory tithe to the Catholic Church, which only concerned Catholics.
The Quebec Act also expanded the province of Quebec to include Labrador in the East and extended the Western boundary to the junction of the Ohio and Mississippi rivers all the way north to Rupert's Land. This expansion had the obvious intent of funneling the fur-trading areas serviced through the St. Laurence into the jurisdiction of Quebec. The land was mainly Indian territory (where the Indians were allied with the French) that was exploitable for the fur trade without endangering Indian land rights and risking war.
American colonists desired to settle these native lands, and therefore listed the Quebec Act as one of the "Insufferable Acts."
4.) Cultural and Religious Isolation: Quebec was the largest British colony in what is now Canada. The language barrier combined with the foreign religion of Catholic Quebec and the history of hostilities from the Seven Years War caused Americans to view the people of Quebec as foes.
5.) Patriot attacks on Canadiens solidified opposition to the American revolution. American Patriot generals Richard Montgomery and Benedit Arnold Attacked Quebec in an attempt to seize Canada from British control (1775). They took Montreal and laid siege (ultimately unsuccessfully) to Quebec City, where British regulars and a few Candien militia defended. The Americans were ill-supplied but stayed till spring, when the British navy sailed up the St. Laurence.
It also became true that in the wartime alliance reached in 1778
between France and the young American republic, neither partner really
wanted to see the other established at Quebec, preferring to have it
left to Britain rather than that either of the two new "friends"
should hold it.
6.) Economic Interests: The merchants of British North-America benefited from the influx of British troops (and money) which powered the offense south from Quebec. The Canadiens also profited from access to the tariff-protected British markets, which far larger New England competitors had forfeited through the act of war. The fur market in particular began to thrive in Canada. The British Navy on the Atlantic and by British military power in the interior both guarded the fur trade.
Businessmen came to recognize that their economic stake in the
imperial system far outweighed any political discontent over the
Quebec Act -- and that Act, after all had re-attached the valuable
southwest fur domains to Canada. Hence the merchants' sense of
commitment increased with the flow of trade on into the 1780s; as they
saw that their St. Lawrence commercial realm was tied both to Britain
and to Canada's own growth westward. Factors of geography and business
interest in effect were shaping the prime leaders of Montreal into
British imperialists and Canadian economic nationalists combined.
7.) Many Loyalists moved to Canada to support the British cause. .
Conclusion: pardon the quotes
As for the mass of French Canadiens in the province (of Quebec), they
began to follow their seigneurial and clerical elites into their own
commitment to the British side. Naturally the Canadiens still put
their distinct community concerns and heritage first; yet they also
concluded that the Americans should not be welcomed, but kept outside.
The self-proclaimed republican "liberators" had simply turned out to
be the same old enemies, les Bostonnais, the Puritans of New England:
stabling horses in Catholic churches during their invasion, paying in
worthless paper money for crops and supplies seized from habitant
farms. The Canadiens did not learn to love their British conquerors as
a result -- why should they? -- but did grow to believe that they were
better off with them. For the provisions of the Quebec Act had
guaranteed French Canada's own special rights and character under
British rule: guarantees which the Americans certainly would not have
given. Instead angry American outcries had greeted the Act because of
the very grants it had made to the "French Papists". Thus for
different but historically sound reasons, neither the Francophone and
Anglophone communities of Quebec province took to the American path of
revolution. They stayed within the remaining British empire -- above
all, to avoid being swallowed up in another emerging empire, that of
the United States.
St. Johns, PEI, and Newfoundland
The little neighbouring Atlantic province, the Island of St. John, was
hardly likely to affect the course of empires. It certainly continued
in British keeping -- although an American privateer raid on
Charlottetown in 1775 carried the acting governor and two officials
off to General Washington, who did not want them, and sent them home.
The big island of Newfoundland also suffered, and more harshly, from
American privateering ravages. But here British garrisons and naval
squadrons still blocked any real threat to imperial control. In any
case, the war years brought the island flourishing times in its
essential cod fishery, particularly for residents, since many of the
visiting overseas fishermen had been drafted into the Royal Navy. Thus
Newfoundland, too, stayed surely within Britain's American empire.
Great Lake Indians
At the other, western end of empire, war spread through the inland
forests below the Great Lakes, from the Iroquois country to the Ohio
and Michigan wilderness. In the upper reaches of New York province,
patriot rebel forces contended fiercely with units raised from
loyal-minded settlers in the area. But further, the Six Nations
Iroquois and their traditional homelands were heavily involved. The
Tuscaroras and Oneidas largely sided with the Americans. The rest of
the Six Nations, and especially the Mohawks, supported the British;
for here old bonds of alliance held strong. They had been well forged
under Sir William Johnson as Indian Superintendent till his death in
1774, to be maintained thereafter by his son and heir, Sir John
Johnson, later to become Superintendent in his own right.
For the most in-depth discussion of this topic I could find see this Canadian Heritage Book (free), which is the source of the quotes and much of the content in this answer.