The nation's unemployment rate shot up to 8 percent last month as the impact of the second recession in two years continued to spread throughout the economy, the Labor Department reported yesterday. It was the highest rate since the deep 1975 recession.

As the rate rose from 7.5 percent in September, the number of jobless workers climbed to 8.5 million in October, up more than 1 million in three months. Among blacks, unemployment hit 16.7 percent, the second consecutive monthly record.

The Reagan administration, which recently predicted that unemployment would peak at 8 percent, said in the wake of yesterday's report that "the rate could move somewhat higher over the next few months before declining as the economy strengthens in 1982."

Despite the rapid worsening of the economy, White House spokesman Larry Speakes said the administration plans no "quick-fix measures" to try to bring the unemployment rate down. He also sought to shift blame for the situation away from the Reagan administration.

"The rise in unemployment is a natural short-term consequence of unwinding the deeply rooted inflation that is imbedded in the economy," Speakes said. He added that "the elements of the president's economic program already in place are sufficient to provide the basis for a strong and lasting recovery which we anticipate will be evident in 1982."

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) took sharp exception to that position. "This recession is a deliberate and conscious policy of this administration," he said in a New York speech. "Now that we are in a recession the administration has no plan to get us out. The reason is that the president is willing to accept a recession and tight money as an acceptable way to fight inflation."

Treasury Secretary Donald T. Regan also said the administration is "very well positioned" to deal with the recession, because personal and business income tax cuts are already in place for 1982. The administration obtained congressional passage of the cuts last summer in an effort to spur saving and investment.

However, the latest survey of business investment intentions released this week by McGraw-Hill shows that spending for new plants and equipment in 1982 will be no higher than this year's after adjustment for inflation.

Such spending might turn out to be even lower, some economists believe, since new orders for capital goods are declining and some previous orders are being canceled.

Meanwhile, the high interest rates that are the major cause of the recession continued to fall. The Federal Reserve has maintained its effort to ease credit conditions as the economy weakens, and the drop in economic activity has begun to reduce business loan demand.

Several major commercial banks lowered their prime lending rate to 17 percent yesterday, and the rate for three-month Treasury bills dropped below 12 percent for the first time in more than a year.

Regan in recent weeks has been critical of the Federal Reserve for falling short of its own targets for growth of the money supply.

But yesterday, in the face of the big jump in unemployment and a $3.3 billion drop in the most closely watched measure of money, Regan pointed to the decline in interest rates and said, "The Fed should stay where it is." He also predicted that the prime rate soon would fall below 17 percent.

The Fed said yesterday that M1-B, which measures currency in circulation and checking deposits at financial institutions, fell to $431.1 billion for the week ended Oct. 28, far below the Fed's target range.

High as the nationwide 8 percent unemployment rate was last month, conditions in a number of states were worse. In Michigan, 12.7 percent of the work force was without jobs, as was 10.4 percent in Ohio. At the other end of the scale, the unemployment rate in Texas was only 5.1 percent.

In Canada, which also released unemployment figures yesterday, the jobless rate edged up to 8.3 percent from 8.2. The post-World War II record for Canada is 8.6 percent.

The last time 8.5 million Americans were out of work was in 1939. That was a much larger proportion of the labor force, of course. The unemployment rate was 17.2 percent. The only other time since 1942 that the unemployment rate for a single month was 8 percent or higher was during the 1975 recession, when it peaked at 9.2 percent.

In October, the number of persons working part-time because their hours were cut back or because they were unable to obtain full-time work rose to a record 5 million, the Labor Department said.

Reflecting the way the recession has spread throughout the economy, only one-third of 172 industries reporting said they increased their number of employes last month.

The deteriorating job picture was underscored by the increase in unemployment among adult men, whose jobless rate jumped from 6.2 percent to 6.7 percent. For the second straight month, the rate for blue-collar workers rose sharply, this time to 11 percent.

The rate for adult women climbed only 0.2 percentage points to 7.0 percent. Unemployment among teen-agers rose from 19.3 percent to 20.6 percent.