Scarcely had the celebration of American daring and intelligence and military prowess begun when it was overtaken by a wave of bitterness over the various ways in which friends of the United States let it down in the Achille Lauro affair. American relations with these countries are too important to be permanently damaged, but the bruising is there and almost certainly, in respect to terrorism, the result will underline a tendency toward unilateral American action in an enterprise where international cooperation ought to be the rule.

President Mubarak pronounced himself "wounded" by the American interception, and he must answer to a public already broadly skeptical of Egypt's American tie. No one wishes to complicate life for Cairo's struggling moderate leadership. Yet few can accept its confidence that the PLO, which increasingly seems the political if not also the operational sponsor of the four terrorists, could be entrusted with prosecuting them. Surely Mr. Mubarak could see why President Reagan had to act as he did.

From the Italians, who fight terror on home ground bravely, it was not unreasonable to expect partnership here with their democratic NATO ally. But Rome deferred to its investment in a cultivation of the PLO -- a second-level line of foreign policy questioned even within the governing coalition. The Reagan administration had all too good reason to express -- at the ungodly hour of 1:30 a.m. on Sunday -- its dismay at Italy's refusal at least to inspect the American evidence for holding the accused mastermind, Mohammed Abbas.

The United States has a strategic interest in Yugoslavia, which has even more of a strategic interest in the United States. But Yugoslavia had a special additional reason -- its own difficult terrorist problem, arising from elements the communists defeated in taking power -- for cooperating in this instance. In fact, very few countries have a greater need for international cooperation in combatting terrorism. This is the consideration Belgrade set aside when it expedited Mr. Abbas' flight.

In their respective voices, all three of these countries argue that the requirement to engage the PLO in a search for a political solution remains crucial. At the same time, Israel has seized on the incident to try to pull the United States toward the view of the current split Israeli government that the PLO is unfit as a partner for peace. Those who still see the PLO as an interlocutor, however, take on an extra obligation. With their interest and access, they should be the first to act against any suggestion of PLO terrorism. Instead, here, they have been the last.