The Reagan administration does not expect a sharp drop in interest rates as a result of its announcement that it will cut defense spending in order to reduce future budget deficits and therefore federal borrowing, officials said yesterday.

Administration economists believe rates have stayed near record levels for several reasons, only one of which -- a fear of continued big deficits -- could be affected quickly by the prospect that defense spending will not rise as fast as expected. In the short run, one Reagan economist said, the demand of credit will be great enough, compared to what is made available by the Federal Reserve, to keep rates high.

That is exactly what seemed to be happening yesterday in the nation's financial markets, which have become effectively the sternest critics of President Reagan's economic policies. Bond prices continued to slip a bit lower as investors shrugged off the latest shift in policy.

Willard Butcher, chairman of Chase Manhattan Bank, summed up the attitude of many market participants when he predicted that "interest rates will remain high for several years" as the government continues to fight inflation. Butcher, speaking to a Canadian audience, said he sees continued "upward pressure" on rates partly because of the need by the administration to finance "substantial deficits" in the years ahead.

Nevertheless, bankers and analysts widely praised the announcement that planned defense spending might be cut $10 billion in fiscal 1982 and as much as $30 billion in fiscal 1984, when Reagan has promised to balance the budget -- though most of them added a note of skepticism.

The chairman of Manufacturers Hanover Bank, John F. McGillicuddy, declared in a Tokyo speech: "From where I stand, only real and widely perceived progress in reducing the federal deficit is going to overcome unfavorable market psychology and hesitancy on the part of investors. I am encouraged, therefore, to learn that the administration is bringing new scrutiny to the proposed arms buildup as well as preparing another round of nondefense cutbacks."

Allen Sinai of Data Resources Inc., an economic forecasting firm, predicted that "the panic in the markets will be arrested now by what is being talked about." But only as the cuts actually come into effect will short-term interest rates come down substantially, he cautioned.

Meanwhile, the dismay of the administration at the continued high level of rates was underscored by the president in an interview published by Fortune magazine, in which he took what could be considered a swipe at the Federal Reserve.

Asked about remarks by Treasury Secretary Donald T. Regan that interest rates were too high, the president replied, "I think what Don was saying was that we can have and should have some loosening of interest rates because they're now contributing to the inflation we're trying to cure."

Was the president saying that himself, he was asked? "Yes," Reagan said. "I'm willing to say it. But we can't dictate to the Fed."

The president did not address the question of how to achieve lower interest rates while continuing a tight monetary policy, which the administration has encouraged the Federal Reserve to pursue, in order to control inflation.

Alan Greenspan, former chairman of the Council of Economic Advisers, said that cutting defense spending was a wise decision that eventually will lead to lower interest rates as government borrowing needs decline. Greenspan said reducing the 1984 budget deficit from the $60 billion to $70 billion range -- which financial markets now expect -- to a $20 billion range could lower long-term interest rates by 3 or 4 percentage points "and substantially more in the short end of the market."

DRI's Sinai estimated that lopping $10 billion off defense outlays next year could cause short-term interest rates to fall by 1 percentage point or more in addition to whatever other declines might occur. However, he added, such a cut would mean a somewhat weaker economy in 1982 -- an assertion administration economists are not prepared to accept.

Greenspan also said that defense spending cuts of the size under discussion would not necessarily mean a weaker defense posture. "I have always thought that an essential ingredient of national security is a viable economy," he said. "There are real national security trade-offs between, say, an additional wing of F-16's and a lower inflation rate. This is not a zero-sum game."