The Reagan administration has laid the blame for its huge Pentagon budget increase on the deterioration of our armed forces under Jimmy Carter. But there's another reason that nobody wants to talk about -- the attitude of our NATO allies to let the United States foot most of the bill for protecting Western Europe from Soviet aggression.

And in the sacred cause of smooth relations with our allies, Secretary of State Alexander Haig is apparently ready to let his old NATO colleagues off the hook. The administration has scrapped the so-called "3 percent solution," which Carter had promulgated to induce the NATO countries to increase their defense spending by that modest amount. Instead, the United States will meekly continue to bear the major cost of Western Europe's defense needs.

The General Accounting Office made an exhaustive examination of NATO and State Departments records in London, Bonn and Brussells, at the request of House Appropriations Committee members. One difficulty the auditors encountered was that nobody in the Pentagon seems to know exactly what the American contribution to NATO is -- or if they do know, they're not saying.

But one thing is clear. It's not peanuts. The GAO concluded that the U.S. share of the NATO burden may be as much as $65 billion a year, although sources told my associate Lucette Legnado the true figure may be closer to $90 billion.

In teh cost figures they were able to trace, the auditors found that the Defense Department's expenditures in NATO countries have risen 82 percent since 1973. All of that, of course, is in cold cash provided by the American taxpayers. By contrast, the allies' contributions are largely indirect -- "income foregone" rather than actual outlay of money.

In other words, the money th host countries would -- or might -- collect if the U.S. troops weren't occupying their bases is credited as part of the countries' share of the NATO budget. While the United States is putting up coin of the realm, the allies engage in speculative bookkeeping to arrive at their share.

The reason for this peculiar arrangement goes back to the early days of the alliance in the 1950s. When the cost-sharing formulas were first worked out, the U.S. economy was booming. Our European allies were still digging out of the rubble of World War II; the most they could contribute was real estate for bases, plus exemptions from taxes on the land and equipment used by NATO troops.

Congressional critics point out that this lopsided situation no longer exists. If anything, the reverse is true: The American economy is in trouble, while the European countries -- particularly West Germany -- are enjoying relative prosperity.

Outmoded as the original cost-sharing formulas may be, the GAO realizes as a practical matter the difficulties of renegotiating a more equitable distribution of the load. But congressional critics feel an attempt should be made to work out a fairer cost-sharing arrangement.

According to the House defense appropriations subcommittee, one of the cost-sharing provisions that is most overdue for change involves the damage claims made agains the United States by West Germany. The claims cover damage to proterty that occurs during training exercises by U.S. troops -- claims that are ignored by armies in a shooting war, but must be acknowledged by allies in a peacetime situation.

In the past five years, damage claims have increased from $15.6 million to almost $40 million. Although West Germany does chip in something, its contribution is small compared with that made by the United States.

In their own defense, the strategists at Foggy Bottom and the Pentagon say it would be better to suffer the cost-sharing inequities in silence and to encourage the NATO allies to invest the money they save at our expense in military improvements. They also point out that if the United States kicks up too big a fuss, our allies may decide to restrict troop training exercises or rescind favorable provisions of the cost-sharing agreements.

Critics of the current setup are not convinced, however. Our military operations in Europe, after all, are for the protection of our allies.