U.S. executives based in Japan barely concealed their sighs of relief as President Bush and his noisy entourage flew home Friday.

Some of the locally based Americans said the president's four-day visit revealed an undercurrent of impatience, naivete, inconsistency and poor planning on the part of the United States."Bringing the three (U.S.) auto executives made us look like we were begging for something," said John King, the state of Missouri's Japan representative. "This (trip) made us look bad as novices. We heard only what they thought we wanted to hear."

Others officials said they expect few lasting benefits from the trip.

"It was kind of an interesting exercise, but I don't know what it's going to amount to in the long run," said David Hayden, partner with the law firm Livdahl, Gaikokuho, Jimu Bengoshi, an affiliate of the U.S. firm Graham & James.

Americans have not invested the time to understand the calculated way in which Japan carries out its policies, complained K.H. Page, president of Tokyo-based International Marketing Consultants, who has been in the country for more than 30 years as a marketing executive.

Japan, Mr. Page said, executes its trade strategy with purpose, dedication and self-interest.

Japanese executives joined in the criticism, saying the trip's last-minute emphasis on jobs and ensuing emotionalism hurt long-term relations and fostered misunderstanding.

"From the American point of view, we (Japanese) seem to be reluctant and half-hearted," said Toshi Yasuda, general manager and spokesman for Nissan Motor Co. "From the Japanese point of view, America is always pressing Japan to do something, and blaming Japan for their own problems."

Some companies cited the often-repeated U.S. need for a long-term outlook and hard work at the grass-roots level. "American companies try and get results very quickly," said Takamasa Numata, president of Wordstar Japan. ''To Japanese people, they (U.S. companies) seem very impatient."

Mr. Numata said U.S. companies must think longer term, be willing to prove their products in the marketplace and make the necessary investments. The big- stick approach does not bring results, he added.

He conceded that software was an industry that faces fewer non-tariff

barriers because the Japanese industry has not been terribly competitive.

Some observers saw part of a silver lining in the auto agreement, which pledges Japanese carmakers worldwide to boost their use of U.S. parts by up to $10 billion by 1994.

"From my perspective, I think a lot of positive things will come out," said Don Johnson, Tokyo-based manager with the Boston Consulting Group.

Mr. Johnson added that the U.S. trade policy must work to apply continuous, steady long-term pressure on Japan. "There has to be a certain finesse," he said. "You can't just hit them over the head."

Others said the complexity of the situation must be appreciated. Even if non-tariff barriers disappear, the Japanese auto market is saturated and Japanese buyers stress long-term relationships, often caring more about loyalty than price.

"It's not (necessarily) that U.S. products are being consciously excluded," said Mr. Hayden, the attorney. "It's like trying to get shelf space in an American supermarket. You have to shoulder your way into the system."

Without understanding the system, the United States risks hurting itself further, he added.

The opening of the U.S. Toys "R" Us store by President Bush was heralded as a victory for U.S. retailers. In fact Japan's restrictions on large outlets are designed to restrict Japanese department stores, which may become the greatest beneficiaries of the U.S. pressure.

Missouri's Mr. King said he faces frustration at both ends. U.S. companies are, by and large, not interested in international business and it often becomes the job of the states to even get them interested, he said. "There are some very provincial people back in the U.S.," he said.

But patience and sophistication don't always work.

Missouri, the state ranking third in production of auto parts, has been trying to gain access for several years to Japanese car companies' specifications while parts are still being designed. So far the effort has been futile.

"I get the polite brush-off. They say they want to meet, but the words are rather hollow," Mr. King said.