The burden for President Carter's decision last week to postpone production of the neutron bombs fall on the United States' allies in Eruope, Senate Majority Leader Robert C. Byrd (D-W. Va.) said yesterday.

"First we need the decision [by the NATO nations] to deploy" the enhanced-radiation weapon, Byrd said. "What good does it do to produce the weapon if we can't deploy it? We need a show of support from our European allies."

At his regular Saturday news conference, Byrd also said the Senate should wait before considering any changes in the legislation Congress passed last year to shore up the Social Security funds by increasing taxpayers' contributions.

But Byrd reserved his strongest words for the neutron bomb issue.

"Our European friends could have been more vocal in their support for going ahead" with production of the bomb, which kills by radiation rather than the blast and fallout of other nuclear weapons, Byrd said.

"I think it is ironic, if not alarming, that our allies would be willing to play our trump card, one of the weapons most feared by the Soviets, as a throw away in the high-stakes game of national security . . .

"If we're to depend on one another, our defense in Europe must be the stiff backbone, and not the soft underbelly, of our protection."

When the existence of production plans for fitting new 8-inch artillery shells and Lance missile warheads with the neutron weapons became public last June, consultations with the NATO allies about deployment were expected to be perfunctory.

Unanticipated opposition, especially in West Germany, where the weapons would be deployed, caused the negotiations to drag on. Sources have said recently that the Germans agreed to production and deployment but wanted another continental power to second the decision.

Byrd said he would have preferred a decision to go ahead with the neutron warheads, but said he can accept the decision to delay.

"A decision not to produce the neutron warhead would likely jeopardize Senate approval" of a strategic arms limitation treaty, he said.

Byrd said the weapon could be used as a bargaining chip to reduce the Warsaw Pact nations' overwhelming tank superiority in Central Europe. The communist nations outnumber NATO countries in tanks by a factor of more than 2 to 1.

Meanwhile, Byrd said it would be "a serious mistake" to reopen the debate on Social Security tax withholding this year.

"Congress acted last year with courage in the face of a rapidly deteriorating situation," he said, adding that the progressive aspects of increased Social Security taxes, coupled with proposed income tax reductions under the Carter tax program, argue for giving the new Social Security financing system more time to operate before being changed.