The Carter administration considers Japan's recently announced increase in defense spending to be too small and has made the Tokyo government aware of its unhappiness.

Administration sources say State Department officials conveyed that message this week through the embassy in Washington.

In the U.S. view, the 9.7 percent increase for defense approved by the Japanese government July 29 is only about a 1 1/2 or 2 percent real increase in military purchasing power after inflation is taken into account.

In real terms, U.S. officials consider that no more than is actually being spent this year. They say it remains well below the 3 percent real increase that a number of the North Atlantic alliance countries have pledged and the 4 to 5 percent U.S. increase beyond inflation. All of those U.S. and European increases are also made on much larger spending bases to begin with.

The administration reportedly did not ask for any specific percentage increase this week but rather emphasized that it expected Tokyo to have come closer to what other allies are doing.

Similarly, there was said to be Pentagon concern that the level of defense spending would make it difficult or impossible for Japan to meet its newly laid-out five-year defense program that the United States has also been counting on.

Defense Secretary Harold Brown, while shying from setting a specific figure publicly as a proper goal for Japan, has frequently expressed the view that Tokyo clearly is capable of a significant and sustained defense program that would be important for overall western preparedness.

The budget approved by the Japanese government was actually considerably less than the 15 percent sought by Japan's Defense Agency.

Even though Japan's version of the Pentagon fought a losing battle with Tokyo's Ministry of Finance, the Defense Agency was the only one allowed to escape government guidelines that held all other departments to increases of 7.5 percent.

Thus, while the cabinet approved the finance ministry version of the defense budget, the 9.7 percent defense increase is still viewed in Japan as an important political gain reflecting a more generally receptive move for defense.

Japan spends only about 0.9 percent of its gross national product on defense, a tiny figure in comparison to the 5.2 percent in this country. The United States had been hoping Tokyo would climb to 1 percent by 1984, but this week's governmental actions will make that difficult.