Democratic dilemma: the uninformed American public; The American Style of Foreign Policy: Cultural Politics and Foreign Affairs, by Robert Dallek. New York: Alfred A. Knopf. 313 pp. $16.95.

Robert Dallek's writings have focused on 20th-century diplomatic history and political affairs. One of his books, ''Franklin Roosevelt and American Foreign Policy, 1932-1945,'' won the Bancroft Prize in 1980. This most recent book, dedicated to and influenced by Richard Hofstadter, ''. . . is a study of undercurrents, of mood, tone, or milieu, of a climate of feeling that almost imperceptibly insinuates itself into concrete ideas and actions. Like the atmosphere, these matters are not easily described.''

The author argues that Americans have often been less concerned with the world around them than with unresolved tensions at home. The end of the 19th century ushered in a period of American imperialism. He attributes this to events at home: the closing of the frontier and the Industrial Revolution.

Dallek argues that the responsibilities of empire - converting nonbelievers to the ways of democracy - made Americans feel better about the new realities they faced in a land thoroughly explored and increasingly urbanized.

Next, the author attempts to explain why the Progressivism of an earlier period was insufficient to ensure the passage of Wilson's Fourteen Points, but he obscures an important point: Americans were inattentive to these international issues.

Even World War II did not awaken Americans to reality, according to Dallek. That awakening came with the cold war. For example, he suggests that the Truman Doctrine was not so much an oversell by the administration as it was a reflection of how Americans actually felt. It was a typically vague pronouncement; Americans could read into it their own hopes and fears.

But Dallek's analysis wrongly suggests Americans cared about events in Greece or elsewhere. Unfortunately, what encouraged Truman's oversell was that most Americans did not care.

Staunch anticommunism was a way to forge unity at home. ''Americans would all have to stand together against communism,'' President Eisenhower said. President Kennedy also tried to forge unity at home when he said during his Inaugural Address that Americans would ''pay any price, bear any burden, meet any hardship , support any friend, oppose any foe, to assure the survival and success of liberty.''

But President Johnson found it difficult if not impossible to continue this approach. Only his retirement from public life and deescalation of the war moved us back in the direction of a cohesive society.

While Dallek rightly criticizes Nixon's and Kissinger's abuses of power, he does not do justice to their grand design. He does not recognize that this is the first example in his book of American leaders managing the American role in the international system rather than merely reacting to domestic priorities.

Every nation faces the challenges of re sponding to the world around it in a manner that it hopes will be warmly received at home. For weaker nations, this is difficult; they are condemned to react to events that are largely beyond their control. For undemocratic regimes, this is easier; they tend to care less about what folks at home think. For a powerful, democratic regime like the United States, this is a tough challenge indeed, but try it must.

What distorts Americans' view of the world is their historical inattention to the problems of international relations. They cannot, however, do as Dallek suggests: ''detach our problems abroad from our social dilemmas at home.'' This is not in character - as he so eloquently describes it. Nor will this be possible in an increasingly interdependent world. Unemployed auto workers in Michigan are not going to detach international trade problems from their social dilemma. And as long as the United States elects its officials, neither will they.

Dallek has written an important book which every informed American should read. But rather than conclude that domestic problems should be detached from international problems, the reader should ask what more he can do to inform the nation's judgments about the important international issues of the day.