I think that the reason why such a statement can be asserted is because of how the British approached the prospect of war with the Colonists. There were few and a small number of voices that actually took the Colonists as a formidable military force. There was little articulation about how the the Colonial home terrain advantage and their intangible commitment to the cause could enable them to win. The British underestimated this and proceeded into battle with the idea that the conflict would be relatively quick and one that can easily be won with a small flexing of muscle. The British might have stood a better chance of winning if they had taken the Colonists with more gravity.
There are two other considerations to the defeat of the British forces that have not been mentioned:
1. The British were strained financially and militarily as they were engaged in wars on the European front; specifically, Spain and the Dutch Republic went to war with England in the years 1778-1780, threatening an invasion in England, and testing their military prowess with campaigns in Europe. France also went to war with England; France, of course, later aided the American troops.
2. The British, who fought in the classical manner, were unprepared for the almost guerilla-type warfare of the Americans. With their red coats the British marched openly into the fields that his the minutemen and other soldiers who "waited until they saw the whites of their eyes." This unprecedented warfare was not something to which the British were familiar.
I don't completely agree with the above posts, as Yorktown was a pretty decisive victory on the part of the Americans. That being said, the British were often their own worst enemies. They staged a rather brutal invasion of the Carolinas - colonies that were full of loyalists - and through their tactics recruited people for the rebellion.
The British employed thousands of Hessian mercenaries that were also quite brutal to Americans soldiers, murdering them after they had surrendered. These stories helped convince people that the revolution was justified.
Lastly, there was a significant number of loyalist Americans who willingly fought on the British side. They were treated as a secondary militia when, given their knowledge of the people and territory, they could have been used as a much more effective fighting force.
These are just a few examples of how the British lost the war.
Not unlike the United States' departure from Vietnam in the 1970s, Great Britain decided to give up their interests in the Americas rather than pursue an expensive and unpopular war. When the war begain in 1775, Great Britain arguably had the greatest military force in the world. Their armies were mighty--they would soon defeat Napoleon's French masses several decades later--and their navy ruled the seas. By contrast, the colonies had no army or navy. They assembled their forces from scratch and held on for more than six years until French aide helped the new nation turn the tide against the English.
The major reason that you can say this is that the British chose to leave. They still held much of the colonies and they could still have probably held on to the cities and won most of the military engagements that might happen. But they simply got tired of the fighting, gave up, and left.
Even though they lost at Yorktown, the British still had more military power than the Americans, especially at sea. Pretty much any place that touched the water could be controlled by the British.
But there was not a huge amount of support for the war in Great Britain, and the expense got to be too much for them to want to pay given that it did not look like they could win quickly.
The statement that "the revolutionary war was lost by the British rather than won by the Americans" unjustifiable belittles the efforts, sacrifices and the determination of the American people in a hard fought war lasting 8 years.
It is agreed that British were a formidable adversaries, very difficult to defeat. But that is all the more reason for giving greater rather than less credit to the American People. It is important to note that the American war of independence was fought on American land, impacting the common American people. For the British people the war produced no such personal hardships for the common people as it did for the Americans.
There are hardly any wars in the world where every one from a side is vanquished before the other party is considered victorious. A warring party become victorious when the other party is routed and retreats, or decides that holds no prospects of victory, or the costs of further war are not worth the victory, and in response asks for peace.
The surrender on October 19, 1781, of more than 8000 men representing more than a fourth of British forces in North America, represented the start of British defeat. After this the British were not able to offer any major fight, though the war continued for two more years. Fearing that continuation of this war might cause more damage than just loss of their colonies in 13 warring states of USA, British initiated peace talks in 1782, which finally led to signing of the Treaty of Paris on September 3, 1783.