The Senate Finance Committee took a big bite out of President Carter's energy package yesterday as it rejected his proposed tax on gas-guzzling cars by a vote of 11 to 5.

White House press secretary Jody Powell called the action "extremely regrettable" and said any tax bill without the gas-gazzler tax would be "deficient." He said the White House faces several other Senate fights on energy and expects to "win some and lose some.

"The next one could come today when the Finance Committee takes up the proposed wellhead tax on oil, a key part of Carter's plan to save energy. Carter wants to cut use of oil by taxing up its price and rebating the tax to the public. There will be attempts in the committee to kill the tax or use the money to help produce more energy.

Sen. Lloyd Bentsen (D-Tex.) has also served notice that next week he will move in the Finance Committee to kill another tax proposed by Carter, on industrial use of oil and natural gas. This is the other kanor tax proposal Carter has made to save energy.

Still another close battle will be fought on the Senate floor this week on whether to continue price controls on natural gas. Carter wants to continue controls at a higher level. The House sided with the President, and the industry is fighting hard to get even in the Senate, which voted to deregulate natural gas two years ago.

Sen. Henry M. Jackson (D-Wash.) chairman of the Senate Energy Committee, said he had "never seen so much pulling and hauling as on the natural gas issue." Carter has been making telephone calls to senators asking for help, he said.

Supporters of deregulation, believing they are ahead, pressed yesterday for agreement on a time to vote on deregulation. But the President's supporters wouldn't agree. Among other things, they are waiting for the return of five senators on their side who are out of the country and due back today.

The gas-guzzler tax fight isn't over. The tax can be offered as an amendment on the Senate floor. And since the House approved it, the tax will be a matter for negotiation in the House-Senate conference that must finally settle differences whatever the final Senate result.

Carter proposed a tax on big cars that get low gasoline mileage. Last week the Senate voted in another energy bill to ban production after 1979 of cars that get less than 16 miles per gallon. Opponents of the tax said the ban made the tax unnecessary.

The administration preferred the tax to a ban, saying consumers should be given a choice of paying more to get a big car.

Finance Committee Chairman Russell B. Long (D-La.) said his view was a person should be "permitted to buy a guzzler and be required to pay more for it." Long said he would pay a high price to get a big car.

Opponents said the tax, which could rise to $3,856 by 1985 on cars getting less than 12 1/2 miler per gallon, would unfairly hit big families that need big cars.

"What's the difference," asked Sen. Bob Dole (R-Kan.), "between a tax on big cars and a tax on a person who buys a six-bedroom house instead of one-bedroom house? They both use energy."

Only four Democrats, including Long, and Republican Bob Packwood (Ore.) voted against a motion to strike the gas-guzzler tax from the bill.

The committee then voted 9 to 7, again over administration opposition, to strike from the bill a House provision repealing a provision in the tax code that permits a taxpayer who itemizes his deductions to deduct state gasoline taxes. The House provision was not expected to save any energy but was offered on grounds that the government should not reward comsumption of gasoline.

After these two votes, Sen. Daniel Patrick Moynihan (D-N.Y.) observed that "we have not been execssively supportive" of the President. "Before the day is out can't we do one thing the President wants?" he asked.

The committee voted 16 to 1 extend from 1979 to 1985 the 4-cent-a-gallon federal tax on gasoline, which otherwise would drop to 1 1/2 cents.

The Finance Committee also voted 16 to 1 to give a gasoline tax exemption to encourage produciton of gasoline mad ein part form alcohol. For gasoline produced with at least 10 per cent alcohol, the entire four-cent tax would be forgiven if the alcohol were made from agricultural or forestry products. One cent would be given if the alcohol were made from some other product.