The almost universally negative reaction to the invasion of Grenada, including criticism from some of America's closest European allies, has raised the possibility that any advantage the United States might win in the Caribbean will be outweighed by setbacks to worldwide U.S. policy goals.

U.S. officials said yesterday that they do not believe there will be any lasting damage to America's image or diplomatic posture.

They expressed confidence that, as events unfold, most fair-minded people will become convinced that the invasion was a limited operation whose only goals were to safeguard American lives, shield neighboring island republics from anarchy and provide democracy's benefits to the people of Grenada.

But they also acknowledged that, as State Department spokesman John Hughes said, "there are other countries which do not share our view" about whether the intervention was justified. They also conceded that Secretary of State George P. Shultz expects to face some tough and skeptical questioning when he meets in Paris today with the foreign ministers of France, Britain and Italy. All have been critical of the U.S. action.

Much of the criticism appears to reflect concern that the Reagan administration is too willing to use force as an instrument of foreign policy. That could make other nations wary of accepting U.S. leadership on a broad range of issues and strengthen the efforts of the Soviet Union and Cuba to portray themselves as the reasonable, peace-loving parties in their disputes with the United States.

That danger probably is most acute in Latin America, with its ingrained fear of U.S. interventionism. There were signs yesterday that Cuba already is manuevering to turn the loss of its foothold in Grenada to advantage by describing Cuban advisers and construction workers who resisted the invasion as inflicting "a costly moral defeat on the most powerful country in the world, tangled up in a war with one of the smallest states on the planet."

However, the potential problems range far beyond the Western Hemisphere and could affect attitudes in other countries about such diverse issues as U.S. efforts to restore peace in Lebanon and the controversial scheduled deployment in western Europe of U.S. medium-range nuclear missiles.

The three countries whose ministers will meet with Shultz today are the other contributors to the multinational force in Lebanon, and the session's main purpose is to discuss its role in the wake of Sunday's bomb attacks against American and French contingents in Beirut.

In addition, Britain and Italy are scheduled to receive U.S. missiles, and domestic opposition to the deployment is strong in both countries and in West Germany. U.S. officials are known to be concerned about the potential impact of the Grenada situation on western European public opinion when the Soviet Union is trying, through a new missile reduction offer, to stave off deployment.

U.S. officials said privately that Shultz expects to encounter the most trouble with France, which said yesterday that it would support a U.N. resolution to condemn the Grenada intervention and which also sought to distance itself from U.S. policy in Lebanon.

The officials noted, though, that Italy coupled its criticism of the invasion with assurances of continued support for the multinational force. They also said that Britain, despite publicly expressed reservations about the Grenada action, privately had assured Washington that it will oppose any U.N. condemnation move and will cooperate with U.S. efforts to have Grenada's governor general, Sir Paul Scoon, take the lead in forming a provisional government. Scoon is the commonwealth country's link to the British throne.

"The alliance is a family that is closely knit, said state department spokesman Hughes. "Even within a closely knit family, there have been and will be differences. But we think relations are still good."

Administration officials dealing with Latin America and the Caribbean also disputed the idea that the Grenada situation would give Cuba any special advantages as it competes with the United States for influence in the region.

Instead, they said, while the United States inevitably can expect a lot of harsh criticism from Latin countries, they will not necessarily allow their anger to turn them toward Havana, which is unable to offer the trade and aid relationship that most Latin American countries have with the United States.

Some officials said a potentially bigger danger would be a generalized, new Latin American disillusionment with the United States. That happened after U.S. intervention in the Dominican Republic in 1965 and, most analysts agree, was a major factor in the ultimate failure of the Alliance for Progress.

The officials added that danger can be avoided if the United States keeps to its goal of getting out of Grenada quickly and leaving a new atmosphere of peace and democracy. They noted that Latin Americans were harsher in condemning the United States for helping Britain in last year's Falklands war, but that the storm passed quickly and had no real effect on U.S. efforts in Central America or the U.S.-Cuban rivalry.