Sharp increase in food, gasoline and housing costs sent consumer prices soaring 1.1 percent in April, bringing inflation for the last three months to an annual rate of 13.9 percent, the government reported yesterday.

Gasoline prices alone rose a staggering 6 percent over the month, their steepest single rise since a 7.3 percent leap recorded in March 1974 in the midst of the Arab oil embargo. Supermarket prices nationally rose 1 percent in April.

Food prices in the Washington area remained essentially stable last month after rising sharply in February and March. Retail grocery prices here edged up 0.1 percent (Story, Page B1.)

The increase in the overall index nationally came as a shock to White House economists, who had expected retail prices to moderate after earlier declines in wholesale food prices. Officials said they still expect food prices to ease.

The administration reacted by stepping up its price-monitoring efforts. The Agriculture Department began an investigation into food prices, while the Council on Wage and Price Stability announced it is probing oil refiners.

However, chief presidential inflation-fighter Alfred E. Kahn warned that there was "not a hell of a lot" the government could do beyond waiting for its budget-tightening to take effect, and he said the inflation fight now "rests with the consumer."

Asked how the government would respond to consumer complaints about rising prices, Kahn replied: "Buy pork, not beef. Pork went down. Use less gasoline. Don't speculate in new housing."

Kahn also caution that, with further oil-price increases likely and productivity still sluggish, "there is no way we can avoid a decline in our standard of living. All we can do is try to adapt to it."

The Labor Department reported yesterday that the purchasing power of the average worker's hourly earnings has fallen 2.6 percent in the past 12 months, primarily as a result of sharply rising prices.

The April rise marked the fourth month in a row that inflation has continued at a double-digit pace. It was six months ago that the administration's wage-price guidelines program began.

When the guidelines program was launched, officials had asked for six months' time for the effort to show results. Yesterday, Kahn and top presidential economist Charles L. Schultze hedged on questions about its success.

However, AFL-CIO President George Meany flatly declared the wage-price program to be "a flop." Meany said that, while wages have soared at bearly twice the pace that Carter projected.

The 1.1 percent surge in April followed increases of 1 percent in March, 1.2 percent in February and 0.9 percent in January. By contrast, in November and December, the index posted increases of 0.6 percent each month.

Among the sharper rises in April were a 4.1 percent spurt in beef prices, a 4.2 percent increase in fuel oil prices and a 1.3 percent increase in housing prices. Prices of new cars jumped 1.3 percent.

In discussing the price figures yesterday, Kahn blamed the increases on a variety of factors, from continued price increases by the oil-exporting nations to rising mortgage interest rates and a shortage of marketable cattle.

Specifically, however, he said that real-estate speculation by investors seeking big capital gains windfalls made the rise in housing costs worse. And he said gasoline prices and risen "higher than is explicable."

Schultze predicted that food prices still will begin to slow soon, in line with recent farm-price reductions. But he conceded that there still is no end in sight to price rises from industrial and energy prices.

The April increase brought the overall consumer price index to 211.5 percent of its 1967 average. That means it took $211.50 to buy the same goods and services last month that cost $100 12 years ago.