Secretary of Defense-designate Harold Brown yesterday downgraded the chances for military spending cuts and said the Pentagon budget may have increase at a faster rate than inflation in the next few years.

In five hours of testimony before the Senate Armed Services Committee, Brown did not abandon President elect Jimmy Carter's campaign pledge to reduce spending by $5 billion to $7 billion through redeployment and better management. However, he said this goal should be described as "savings rather than cuts" and that such large economies would not be acheived until fiscal year 1979 or later.

Ir rising trends of Soviet military spending continue, these "savings may be more than offset by the need for "real growth" in U. S. military programs, Brown said. He gave no indication of how large a spending increase has in mind, nor was he asked.

While anticipating that the Soviet Union will continue improving its military forces, prompting greater U. S. efforts, Brown warned against overestimating Soviet strategic military power. He said the United States has the ability to destroy the Soviet Union "as a functioning society" even after a Soviet attack and that the highest U. S. priority is to retain this capability.

"Worst case estimates of Soviet power do not do a service to American strength throughout the world," he said in apparent reference to the controversy over a National Intelligence Estimate of Soviet might.

U. S. overestimates of Soviet kept before him at the witness table a note to himself that read: "Keep cool. Say less. Stop." He kept his own advice, coming across as a well-informed, cautious technocrat.

While refering to some of the options, cost studies and amangement techniques of former Defense Secretary Robert S. McNanara - whom Brown served as secretary of the Air Force in the mid-1960s - be made no effort to overwhelm the senators in McNamara-style, speaking to them as a respectful younger man.

Senators praised his demeanor and views and gave indication he will be confirmed without difficulty. The committee is scheduled to receive closed-door testimony today on secret matters from Brown and his designated deputy, businessman Charles Duncan Jr.

Duncan, who was questioned for 25 minutes yesterday, said he plans to be Brown's "alter ego." A second deputy secretary's post, now centered on intelligence matters, will not be filled, Brown said.

In wide-ranging answers covering almost every aspect of Pentagon policy, Brown tolt the Senate committee:

He has to made no decision about the future of the B-1 bomber but undertakes his study of it with the "preconceived notion" it would be a good idea to retain manned bombers in the U. S. strategic forces.

He is opposed to unionization in the military.

He will institute "careful inspection" to make sure military intelligence agencies do not violate citizens' constitutional rights.

The United States should explore the possibilities of an agreement with the Soviet Union to head off a naval arms race in the Indian Ocean.

It should be possible for the United States to "draw down" its sground forces in South Korea after careful consultations with the Korean and Japanese governments, but U. S. airpower there should be retained.

Asked what lessons he and the nation should have learned from the Vietnam war, Brown replied that the United States should be very cautious in expanding foreign policy commitments or undertaking military action beyond "vital security base in a contested area almost guarantees that U. S. intervention would be fruitless, and that if there is weakness in political support at home there is, "no chance" of success.