Despite searches I have had trouble finding a reasonable response to the question from the British side, there is certainly no shortage of literature about what Americans thought. Did losing this big colony and being stuck with Quebec worry or greatly upset people like George III and the PM?
It varied, because the British people were quite divided on the merits of the war in America. There was a substantial body of opinion in the UK at all levels of society that held that the American colonist's cause was essentially just and that their independence was justified under the circumstances.
The moods of the elite I'm less sure about, but I wonder what you mean about being 'stuck with Quebec'? The British had controlled Quebec for a long time before the end of the revolutionary war.
Anyway, a good source for English public opinion is Keith Philips' The Cousins Wars.