The papacy wasn't too pleased, but it wasn't about Germany unifying exactly. The papacy had lost the vast majority of the territory of the Papal States to the process of Italian unification in 1860-61, leaving it with just Rome within its control. The only thing that kept the Italians from claiming the city they wanted as their capital was a contingent of troops in the city that were provided by Napoleon III. Unwilling to risk a clash with the French, the nascent Italian state waited.

Then--as part of German unification--the Franco-Prussian war broke out. Napoleon III withdrew his troops and the Italians took their chance. Token resistance was provided by the papal defenders. The Italians took most of Rome but left the Vatican untouched. Pius IX did not recognize the new situation as legitimate, and refused to acknowledge the Law of Guarantees that the Italians offered in 1871. The pope declared himself a "prisoner of the Vatican" and urged Catholics to not participate in the new government. The result was a standoff between the papacy and the new Italian state that lasted until 1929 when the Lateran Concordat finally settled the "Roman Question"--creating the Vatican City and normalizing relations between the two governments.

So the pope's displeasure was a bit remote: the Papal States were in a conflict with the process of Italian unification, the Italians didn't want to attack Rome because it held a contingent of French troops, those French troops were removed because of the German assault during the Franco-Prussian war, which led to the Italians taking Rome (except the Vatican), and losing control of Rome perturbed the pontiff.

I'm especially interested in how the British reacted.

For Britain, her traditional, hereditary enemy had been humbled. For many in people in Britain, the vulgar bombast of Napoleon III and the tawdry glitz of his Empire had been exposed by Prussia. During the 1850s and 60s there were invasion scares concerning the possibility of France's steam-powered ships being able to transport tens of thousands of soldiers across the Channel over night. Many people believed that French imperialism had caused the war.

The British government at the time was a Liberal administration under William Gladstone. Gladstone was outraged at Bismarck's annexation of Alsace-Lorraine without reference to the wishes of its inhabitants. The Foreign Secretary Lord Granville said Gladstone was "much oppressed with the idea that this transfer of human beings like chattels should go forward without any voice from collective Europe". However Gladstone was unable to persuade his Cabinet of the necessity of organising other neutral states in protesting against the annexation. The Cabinet did not want an intervention that was not backed by force. Gladstone retaliated by writing an anonymous article for the Edinburgh Review in which he claimed that there could not be a friendly relationship with Germany if they held over one million people against their will. However the Daily News soon leaked Gladstone's authorship, which led to much mockery that the British government's response to one of the most important events in modern European history was a tentative review article.

Gladstone, as an internationalist liberal, was alarmed at the undemocratic nature of the annexation and the growth of "Bismarckism, militarism, and retrograde political morality". However his attempt to organise a collective protest against this from the neutral European powers did not materialise.

However Disraeli's reaction deserves quotation as a remarkably prescient appreciation of what had happened:

Let me impress upon the attention of the House the character of this war between France and Germany. It is no common war, like the war between Prussia and Austria, or like the Italian war in which France was engaged some years ago; nor is it like the Crimean War. This war represents the German revolution, a greater political event than the French revolution of last century. I don't say a greater, or as great a social event. What its social consequences may be are in the future. Not a single principle in the management of our foreign affairs, accepted by all statesmen for guidance up to six months ago, any longer exists. There is not a diplomatic tradition which has not been swept away. You have a new world, new influences at work, new and unknown objects and dangers with which to cope, at present involved in that obscurity incident to novelty in such affairs. We used to have discussions in this House about the balance of power. Lord Palmerston, eminently a practical man, trimmed the ship of State and shaped its policy with a view to preserve an equilibrium in Europe. ... But what has really come to pass? The balance of power has been entirely destroyed, and the country which suffers most, and feels the effects of this great change, is England.

What you also see happening in Britain is the rise of invasion literature (The Battle of Dorking is the most famous). Not all of them portrayed Germany as the invader (sometimes it was France) but increasingly the older view of Germany as a land of culture (Goethe etc.) is superseded by image of Germany as dominated by Prussian militarism and a reactionary Junker class.

Sources: Richard Shannon, Gladstone: Heroic Minister: 1865-1898 (Allen Lane, 1999). William Flavelle Monypenny and George Earle Buckle, The Life of Benjamin Disraeli, Earl of Beaconsfield. Volume II. 1860–1881 (London: John Murray, 1929).