Despite the efforts of budget-conscious agencies looking for every penny they can save, the federal government's energy bill keeps spiraling upward.

Last year energy costs for federal agencies hit a record $13.7 billion, about $1 billion more than the year before, despite a 4 percent drop in consumption, according to Energy Department statistics.

"Costs are up, true, but the proof of the government's program is in the trends toward continued energy conservation despite the change in administrations," said J.W. (Bill) Bethea, the DOE's director of federal energy conservation programs. "When you consider the growth of the Defense Department, that's pretty good."

The Reagan administration relaxed most of the conservation guidelines that the Carter administration had imposed on the government and private industry, counting on market forces--primarily higher prices--to encourage conservation.

The federal budget crunch has encouraged agencies to conserve but has also cut the government's ability to monitor their consumption.

In 1975, two years after the Arab oil embargo, the nation's consumption reached its low point: 70.7 quadrillion BTUs (or quads). Consumption grew with the economy to a peak of 78.9 quads in 1979, then declined to 70.8 quads by 1982.

On the federal side, consumption followed a similar pattern, although the government achieved a decrease in consumption between 1975 and 1982. According to Bethea, the government cut its use of fuels for facilities 9.4 percent, but increased its use of fuel for cars, ships and aircraft 5 percent.

The changing emphasis of the Reagan administration, however, has left bureaucrats in the conservation program somewhat exasperated, according to Bethea. He and his six-person staff are survivors of RIF reassignments and do little more than "number-crunching," he said. No one on the staff worked in that office before 1981.

He added, "We have not made a projection of federal energy costs for the current year because of the staffing problem." Instead, the office must rely on information derived from monthly meetings with officials concerned with energy use at the largest agencies.

The federal government's top energy miser has been NASA, which cut consumption 18.6 percent from 1975-1982. Other agencies that registered big drops were the U.S. Postal Service, 16.6 percent; the Agriculture Department, 13 percent, and the Interior Department, 12.8 percent.

The Defense Department, which accounts for more than half the government's energy use, cut its consumption 1.4 percent overall and its consumption in buildings 14.5 percent between 1975 and 1981. During that period, the General Services Administration cut its energy use overall 9.4 percent and in buildings 9.8 percent.

Conservation measures in federal buildings have been the biggest success, cutting energy use 14.4 percent since 1975. That figure does not include the Defense Department's figures. President Carter's goal was a 20 percent cut in that area by 1985.

Some GSA officials are concerned that President Reagan's order to cut back federal office space may make it harder for agencies to conserve in the future.

"If planners are not careful when they cut federal workers back to 135 square feet of space, they will cause energy costs to increase," said GSA building management chief Paul J. Chistolini. For example, he said, redesigning an office with floor-to-ceiling dividers could disrupt normal ventilation patterns.

Compounding the problem is the explosion of electronic office equipment and computers in federal offices.

"Besides increasing costs, the electric load and the heat generated by equipment is causing us to use more energy," said James G. Whitlock, the GSA's regional public building commissioner here.

Agency conservation measures have included installing solar panels, shifting janitorial crews to daytime work and adding transparent, heat-reflecting, plastic screens to glass windows and electronic devices that turn off indoor lights when natural light is sufficient.

In fiscal 1982, the GSA spent $289.2 million on energy for public buildings and $7.7 million on conservation measures.