A few months ago, the organizations that speak for the nation's 100,000 public schools were riding high.

There was a new Department of Education, committed to federal spending for the public schools and to giving the schools a high profile in the federal structure.

In the wake of the Reagan victory, however, this ebullient mood has been replaced by uncertainty over federal aid and anxiety over early signs of a new emphasis on private education.

"There's a good bit of apprehension at the moment over what all this means," said Terry Herndon, executive director of the National Education Association, which backed Carter and led the lobbying for an education department.

Consider, for example, these developments:

Lorelei Kinder, the Pasadena, Calif., woman who is directing the transition for Reagan at the Department of Education is almost completely unknown by educational interest groups based here. Most of her experience has been as a political organizer and administrator. In an interview this week she said that her own two children "have always attended private school."

Thomas Patrick Melady, the president of a university founded by the Catholic Church, was mentioned in the Nov. 10 issue of the Chronicle of Higher Education as a contender for the post of secretary of education. Melady opposed the creation of the department and supports tax credits for people sending children to parochial or private schools -- a diversion of aid that is anathema to public schools.

Another possible contender for the job, Arizonan Carolyn Warner, has sent all her six children to public school and says she opposes tuition tax credits. But Warner adds that her concern is that the credits would end up "destroying private schools," whose educational role she values. Her reasoning is that such tuition aid ultimately would burden private and parochial schools with bureaucratic and regulatory requirements that would "alter them beyond recognition"

There are other signs that elementary and secondary education could emerge as a major political and ideological battleground over the next four years.

In addition to the tax credits which the Carter administration opposes, the GOP platform calls for an end to forced busing of children to achieve racial desegregation, for restoration of voluntary, nondenominational prayer in schools and halt to "regulatory vendettas" against independent [private] schools.

At the same time, Reagan has publicly supported block grants to the states to take the place of the federally run programs that have channeled money to the schools since the middle of the 1960s.

Kinder, who is the only woman directing the transition for Reagan at the Cabinet level, said this week that her job is not to set policy but to pick a team that will be able to "assess and evaluate" the Department of Education.

Kinder's background is mainly in politics rather than education. She directed the Reagan primary effort in California and Kansas and then put together a national effort to bring women, blacks and Hispanics into the Reagan camp for the general election. A Reagan aide said that "if you're a Republican in California who doesn't know Lorelei Kinder you're nowhere." During the time that Reagan was governor in California, Kinder worked in the legislature for John Harmer, a conservative who was active in education.

Others describe Kinder as a pragmatist rather than a political ideologue. The Nov. 22 issue of the national conservative weekly Human Events criticizes Kinder for "packing" Reagan's women's policy board with "pro-ERA and pro-abortion women."

Kinder said that while she personally opposes abortion and the Equal Rights Amendment, "people can disagree on specific issues and still agree that the government shouldn't have policies that encourage the breakup of families." Like Reagan, Kinder is divorced and remarried. She said she chose private schools for her children because "when you go back to the work force as a single parent, you want to know your child is secure in a school situation."

In her integrated neighborhood on Prospect Boulevard in Pasadena, "we go to private schools and public schools but everyone comes home in the afternoon and plays with each other."

Melady, president of Sacred Heart University in Bridgeport, Conn., said that he had not been formally approached with regard to a position at the Department of Education. He is a member of the Reagan task force on educational policy. Sacred Heart was founded by the Catholic diocese but is now privately financed, Melady said.