The Carter administration has registered its unhappiness with the Bonn government about West Germany's unwillingness to meet its pledge to the North Atlantic military alliance to boost real defense spending next year by 3 percent beyond inflation.

The West Germans, whose 495,000-man armed force provides the backbone of NATO's defenses in Central Europe, will increase real defense spending by about 1.5 percent next year, according to Defense Minister Hans Apel. But even those figures are suspect because inflation here is running higher than had been forecast.

Bonn's decision, and its apparent determination to stand by it, is being viewed with special concern by American officials because of West Germany's key role in the alliance and the possible effect Bonn's stance will have in both the U.S. Congress and other Western parliaments.

U.S. Defense Secretary Harold Brown, testifying Wednesday before Congress on behalf of the administration's effort's to live up to the 3 percent pledge, said, "Our efforts to get our allies to do their part will be fatally undermined if we, as leaders of the alliance, don't meet the 3 percent ourselves." The U.S. Senate Tuesday approved a 5 percent real increase in defense spending.

Bonn's position could prove to be highly embarrassing, especially since West Germany has one of the world's strongest economies, lowest inflation rates, is directly on the front line facing the Warsaw Pact nations and has been a bulwark of fiscal support for NATO for many years.

In 1977, the 13 NATO military partners agreed, in a nonbinding pledge, to commit themselves to the annual 3 percent real increase through 1983. This generally has been adhered to by the larger countries, but not by countries such as Turkey, Greece, Italy, the Netherlands and Portugal.

Just four months ago, the NATO countries, including West Germany, reaffirmed their commitment in a communique at the semiannual ministers' meeting in Brussels.

By July, however, when the draft of the new 1980 Bonn budget was published, it was clear that Bonn would not meet the commitment this year.

The figures showed the defense budget increasing from about $20.4 billion in 1979 to $21 billion in 1980, about a 3 percent rise. When some additional personnel costs expected later in the year are included, the increase, according to Apel, rises to 4.4 percent. Last year, West German inflation was only 2.8 percent.

A 3 percent estimate was used for 1980, accounting for Apel's estimate of 1.5 percent real growth next year. Actually, however, inflation is now forecast at about 4.5 percent, which suggests that, in real terms, Bonn will have no increase in defense spending.

Since July, U.S. officials have been waiting for something to happen. Brown has expressed Washington's concerns privately to Apel and they also have been relayed by the U.S. Embassy here. Earlier this month, however, Apel and Finance Minister Hans Matthoefer both made it clear -- during a parliamentary debate that Washington was counting on to change the picture -- that there would be no change.

Matthoefer, in July, had said Bonn did not always have to play the role of a "model boy," when pressed about the defense budget. Next year is an election year here and he and Apel both have said inflationary pressures and a federal debt that already is high make this a tight year.

Apel also argues strongly that West German security is not threatened and that the most militarily significant portion of the military budget -- for procurement of equipment and weapons -- is going up by 7.7 percent.