In order to make this argument, you will need to think of the French and Indian War as part of the larger, worldwide Seven Years' War. You will also need to think of financial, as opposed to physical, sacrifice. When looked at in these ways, the war demanded more sacrifices on the part of the people in England.
The Seven Years' War is said to have costed Britain 161 million pounds. Although comparison to today's money is difficult to do with accuracy, this can be estimated to be in the region of $29 billion. This was a huge sum of money. This money was raised by taxing the people in Britain, not those in America.
Of course, the colonists in America would not have seen things this way. They would have focused on the costs of the North American part of the war exclusively. They would have also focused on the fact that many of them were fighting and dying in the war. But from the British perspective, the financial costs of the whole war (and the fact that many Britons died worldwide) would have seemed more important.
For these reasons, the British would have felt that they bore more of the burden in this war. This would have contributed to their feeling that the colonists should be made to pay for some of the costs of the war.