This represented a familiar pattern of how competing empires both viewed and used Native Americans. Depopulated and driven west, native tribes often felt they had little choice but to ally with the lesser of two devils, the French, in an attempt to win back tribal lands that had been taken from them. The French, far from progressive themselves, needed the tribes since they were outnumbered, and the natives knew the frontier better than anyone.
Even if the French had won, it is doubtful the Native Americans position would have improved, as most of the English settlers would have remained, and once French objectives were achieved, they would have had no more use for the tribes. It was a lose-lose situation for them.
Actually, Native Americans fought on both the French and Indian sides of the war; in fact it actually began as a dispute between two Indian tribes and culminated in a world war. The Iroquois fought with the British not so much because they were enamored with the British, but because they hated the Hurons who fought on the French side.
The war had a very unlikely beginning. British colonists were moving into the Ohio River valley which was claimed by France. The French put down survey markers to mark the territory as their own; however the Native Americans promptly pulled up the markers. The French then began erecting forts in the area. This would have left British North America as a tiny strip along the Atlantic coast. George Washington, then a 28 year old colonel in the British Army, was sent to get rid of the French, and carried a number of Native Americans with him to help him find the French. Washington personally had no use for Native Americans, once commenting that there was "nothing human about them but the shape."
Washington's men encountered a French garrison commanded by one Joseph de Villiers Joumonville, and a brief skirmish ensued during which Joumonville was wounded. The French asked for a truce, and the wounded Joumonville produced a letter which he said would clear up the matter. Washington could not read French, and turned to his interpreter. While he was turned away, an Indian Chieftain with him named Tanaghrisson, and who was angry at the presence of Native Americans with the French, yelled in French Tu n'est pas encore mort, mon pere ("Thou art not yet dead, my father,") sunk his tomahawk into Jumonville's skull, and washed his hands in the man's brains. This was a signal to the Indians with Washington who then killed all the French but one. Washington was forced to withdraw, but was later forced to surrender to a larger French garrison. From this single incident, the French and Indian War, commonly known as the Seven Years War, began.
Native Americans ignited the spark which led to the war; but were neither rewarded nor punished in the Treaty of Paris of 1763 which ended it. The Treaty was wholly a European affair. The bad news for Native Americans was it ensured British presence in North America.
It certainly an ending of tragic proportions for the Native Americans. The Native Americans went "all in" against the Colonists and believed that siding with the French would allow them to regain land taken. This turned out to be a fairly bad conclusion for them as the Colonists won. It was particularly challenging to the Native Americans because their alliance with the French was never to be evident again in the New World. At the same time, it marked the point of decline for the entire culture, as increasingly the Colonists felt empowered to move Westward, overtaking Native American lands in the process. In terms of tragedy, the outcome of the war acquired a very dramatic element because Native Americans, who believed in the collective notion of the good as opposed to the settler self interest, found their own value systems invalidated and negated by the outcome of the war. This "ultimate dispossession" is fairly tragic in both historical and dramatic terms.
So are you asking why this statement is true? If so, it is true to some extent because the Native Americans who backed the British then found themselves faced with British colonists who wanted to expand into the lands claimed by the Native Americans.
Please note that not all of the Native Americans sided with the British. The war was between the British and their Indian allies and the French and their Indian allies. So some of the Native Americans did not come out on the winning side.
But even those who had backed the British did not really benefit. After the French left North America, the British settlers felt that they should be able to settle the lands that had formerly been occupied by the French or that had been too near the French to be safe. Much of this land was claimed by the Native Americans. After the ending of the war they helped to win, they were faced with a movement of settlers onto their land, one which eventually forced them off of most of that land.
In that way, the war turned out badly even for those Indians who backed the winners.