Under American pressure, the West German government today announced a projected 2.2 percent increase in real defense spending for next year, exceeding initial draft figures but still falling short of the 3 percent target pledged earlier by all Atlantic Alliance members.

Although later budget supplementals have been hinted at, bringing the West German military total closer to the NATO mark, Bonn's shortfall for the moment is expected to make more difficult efforts by Washington to nudge smaller alliance states to stay faithful to their three-year-old defense commitments as well.

Defending the governor's decision, Finance Minister Hans Matthofer said today he was "increasingly impatient with these mechanistic yardsticks" for determining military strength. In Bonn's view, it is not how much is spent but how, and Matthofer argued that West Germany's conscript Army -- West Europe's largest conventional force -- is highly cost effective.

In an evident reference to America's nondraft Army, Matthofer said, in English, that West Germany got "more bang for the buck."

The draft budget initially had slated a real increase of a few tenths of 1 percent for defense. But pleas from Defense Minister Hans Apel, together with Chancellor Helmut Schmidt's own renewed promises last month that his government would try to reach the 3 percent mark, shook an additional 700 million West German marks ($350 million) loose.

The resulting proposed budget for defense, which was the only item to be increased in a Cabinet session yesterday beyond its initial figure, now totals $20.6 billion, a nominal increase of 6.2 percent over this year. The government has forecast a cost of living increase of about 4 percent for next year, meaning roughly a gain in military spending in real terms of 2.2 percent. y

A weakened West German economy and, for Bonn officials, and increasingly worrisome national debt heightened government interest in limiting some spending next year.

Overall, the 1981 budget provides for federal spending of $112.3 billion, an increase of 4.3 percent over this year.

Calculating just how much West Germany will end up spending on defense in real terms involves more than a little mathematical dexterity. It is complicated above all by deciding on an appropriate inflation rate to use as deflator, since defense items tend to change in price at a rate different from those items used to compute the general cost of living.

NATO's 3 percent target was agreed to in 1977 by member nations in order to help finance a long list of defense improvements intended to maintain Western military strength in the face of much-improved Soviet forces.

But this alliance pledge was ill-conceived, say Bonn officials, who now maintain that a truer benchmark of military readiness should be an efficiency standard rather than a spending one.

Soviet defense expenditure, meanwhile, has been growing annually at 4 to 5 percent in real terms, according to NATO estimates. The incoming Reagan administration has talked of upping U.S. defense spending by more than 5 percent in real terms next year.