There was a fair bit of sympathy for the American cause in the UK. The Whig leader in Parliament (the more liberal party of the time) Charles James Fox even paraded around in the blue of Washington's army. The colonists were seen by most as the same people to the British or as the Governor of Quebec put it 'brothers or first cousins'. Of course, not all held these opinions (I'm looking at you Samuel Johnson).

Also by the time of the American Revolution the Caribbean colonies were still of far more economic worth to the UK and it was not a silly assumption at the time to believe this would continue for the foreseeable future.

In fact, it is reasonable to make the assertion that the people that considered the success of the revolution 'a big loss' would have been the 100,000 colonists who emigrated north to the Canadian colonies more so than any British back in Europe.

I would suggest that, on balance, the American colonies were a net loss to the UK by the later 18th Century. the war in N.America against the French was very expensive, hence the British governments attempt to get back at least some of the costs by raising new taxes in the Colonies. The colonists had profited significantly by the war, with considerable expansion of the potential area to settle in the Americas, as well as the reduction of the danger to the Colonists from French/Indian raids. The protection of the frontier by British troops was also very expensive, and most, if not all of the taxation collected in the Colonies was spent there. I would suggest, therefore, that the loss of the Colonies wasn't really a serious financial loss to the Crown.

Among the English public there was a lot of sympathy for the American cause, but among the elites the loss of American Colonies came as a shock. Among the Tory Aristocrats that still pushed for the war as it became unpopular they held fast to exiled loyalists who said 70% of the American Colonists loyal, even though historians and English Commanders on the ground at the time found the number of loyalists to be less than 1/5th of the Colonial population! Much like the American war in Vietnam the defeat was seen as humiliating. However because the great struggle against Revolutionary France and Napoleon followed in the next decade the Succession of the colonies was soon forgotten, much like how WWI faded in American popular memory after the "good" war: WWII. Many of the British Generals who were humiliated at the hands of Washington retired with honors and laurels fighting Napoleon's armies. If you want to read into this I would recommend The Men who Lost America