President Carter won the expected endorsement of his reelection bid yesterday from the National Education Association, the 1.8-million-member teachers' union.

Backing of the president was approved by 77 percent of the more than 7,000 delegates at NEA's annual convention in Los Angeles -- slightly lower than the 78.5 percent margin by which Carter won NEA's first-ever endorsement four years ago.

The secret-ballot vote was simply a yes-or-no referendum on the recommendations from the union's board of directors and political-action arm that Carter be endorsed. Supporters of Sen. Edward M. Kennedy, Carter's challenger for the Democratic nomination, Ronald Reagan, the prospective Republican nominee and independent candidate John B. Anderson all contributed to the "no" vote, but were not allowed to record their individual preferences.

NEA staff members have been working with the Carter campaign since last fall, and the organization has elected more than 430 of its members as delegates and alternates to the Democratic National Convention -- all but a few of them Carter supporters. Carter addressed the NEA convention Thursday, but because the visit was technically nonpolitical, he did not comment directly on the union's support of his candidacy.