Employes at one of the nation's largest shipbuilding firms engaged in "regular, systematic" false billing that cost the Navy thousands and perhaps millions of dollars during the past several years, according to a new Senate investigation.

The alleged mischarging at the Litton Industries Ingalls Shipyard in Pascagoula, Miss., which has built more Navy ships during the past decade than any other contractor, could distort the cost of the major shipbuilding program the Reagan administration has begun, senators said at a hearing yesterday.

"The problem of mischarging has been a significant one," said Sen. William V. Roth Jr. (R-Del.), chairman of the Governmental Affairs permanent subcommittee on investigations. Roth said the practice goes on at other contractors and shipbuilders and amounts to "stealing from the government."

Navy and shipyard officials acknowledged during the hearings yesterday and Tuesday that there had been false billing. But they said the extent of the problem was so small compared with the size of the shipbuilding contracts that it had no effect on the Navy's costs or the shipbuilder's profits. "We're talking about a very, very small number," said Leonard Erb, president of the Litton Ingalls Shipbulding Division. "Unacceptable in my view, but let's not draw conclusions that are not there."

The subcommittee's investigation, which was triggered by an independent inquiry by the non-profit Better Government Association, also found that the Navy spent thousands of dollars furnishing captains' quarters on new ships with items such as a $14,000 leather sofa, a $13,500 custom-made bookcase and planter equipped with plants and grow light and a $930 brass and plexiglass telephone stand.

"I must conclude that our controls were not as tight as they ought to be and the judgment applied was by no means as mature as it should have been," Assistant Secretary of the Navy George A. Sawyer testified yesterday. Sawyer said new regulations had been issued to prevent such extravagant purchases of furnishings in the future, while an investigation is continuing into past practices.

The subcommittee devoted most of its attention, however, to the mischarging, under which the shipyard allegedly would work for one customer while billing another. In one case, which Ingalls recently agreed to settle by paying the Navy $137,000, the shipyard charged the Navy for work it performed on commercial oil drilling rigs.

Roth said the shipyard also may have juggled costs among Navy accounts, which could disguise the cost of certain prototype ships.

Ingalls acknowledged, for instance, that in one case its employes worked on the $930 million Ticonderoga, the first of a new type of cruiser, while claiming to work on two destroyers that were being built for less than their allotted budget.

The result, according to the subcommittee report, would be to allow Ingalls to get paid for all its work while appearing to build the Ticonderoga below cost. That would put the shipyard in a good position to win future cruiser contracts, and the Navy has, in fact, awarded Ingalls non-competitive contracts to build four more Ticonderoga class cruisers.

Sawyer said yesterday he has directed a task force to review the allegations of mischarging, but believes them to represent a minuscule portion of the Ticonderoga budget. He said Ingalls did an "outstanding" job overall and is likely to win additional shipbuilding contracts this year.