THE FEDERAL Reserve System speaks softly, but the message deserves an attentive hearing. Anthony Solomon, the president of the New York Federal Reserve Bank, delivered a carefully phrased caution the other day on the subject of inflation. He fully endores President Reagan's economic goals, but he expressed the financial world's rising uneasiness about the manner in which the administration is pursuing them.

In its more lyrical manifestations, the supply-side theory holds that tight control of the money supply can, alone, end inflation. The Federal Reserve is in charge of the money supply, and this kind of talk dismays it profoundly because it implies that nothing else -- taxes, deficits, wages -- makes any difference at all.

Mr. Solomon was responding to a series of developments beginning last month, when the president published his economic program. People immediately noted that its monetary and fiscal positions were inconsistent. The monetary policy was to be tight, with less growth of the money supply next year than this year, but the fiscal policy was to remain expansive. While the administration is cutting the budget, it also wants to cut revenues, now, and far into the future, with its three years of reductions in tax rates. The difference between spending and revenues -- the deficit -- would come down very little next year, even under the administration's forecasts.

Then, 10 days ago, New York began to hear about the Congressional Budget Office's estimate that the deficity was understated by perhaps $22 billion. If correct, that would mean a deficit next year that was moving, not slightly downward, but sharply upward. Meanwhile, the administration is stepping up its campaign for those three successive years of tax cuts.

There's much more to inflation than budget deficits alone, and Mr. Solomon also emphasized the importance of international competition in holding down prices. It was an obvious reference to the continuing debate within the administration over automobiles from Japan.

To put the point more bluntly than Mr. Solomon did, monetary policy belongs to the Federal Reserve and the Federal Reserve is determined to hold to its targets. If Mr. Reagan loses control of the budget deficit, the immediate result will be soaring and swooping interest rates in the style of Mr. Carter's last year in office. If Mr. Reagan tries to ease himself out of a political dilemna by resorting to quotas on Japanese cars, inflation will leap ahead regardless of monetary policy. Theoretically, a rigid monetary policy could eventually quench the inflation. But it is questionable whether American society could endure the distress -- the drop in production, in profits, in wages and in jobs -- if the whole job were left to the Federal Reserve alone.