President Carter, criticized last year for not paying enough attention to education, intends to seek an increase in federal aid to education next year as large as any since the early days of Lyndon B. Johnson's Great Society program.

Carter told Congress last night that his 1979 budget will call for a 14 percent increase in federal education spending.

Most of the increase, he said, will be directed toward disadvantaged children, financial aid for middle-class college students and assistance to states for educating the handicapped.

He also formally anounced that he will, as previously reported, press for a new cabinet-level department of education, which he promised to do in his election campaign.

This was considered a setback for Health, Education and Welfare Secretary Joseph A. Califano Jr. who had opposed such a department.

The administration, Carter said, will also introduced legislation to replace or revise expiring federal education programs, chiefly the Elementary and Secondary Education Act.

The moves are expected to shore up an undercurrent of uneasiness among education groups during the past year over what they considered a lackluster preformance on educational issues.

The increase, sources said, would raise the federal government's education expenditure to $11.6 billion. A year ago, Carter's budget called for $9.1 billion for education, an amount Congress, despite Carter's whishes, raised to more than $10 billion.

The administration, it was learned, has also come up with a rhetorical vechile to answer public uneasiness over problems in the nation's schools. It's a new piece of legislation called the Educational Quality Act.

The act, still being drafted in HEW, calls for an increase in spending under $200 million, a modest amount by federal standards. It basically is a consolidation of a series of small existing programs along with a few pet projects of Califano and Commissioner of Education Ernest Boyer.

The emphasis on quality, however, "should be popular" in Congress, a memo Califano sent to Carter said.

Califano and other officials have refused to comment on the proposed Education Quality Act. But the December memo to Carter said it would consolidate a series of existion efforts, including the Right to Read programs, which "be revised to deal broadly with federal leadership in basic skills," drug abuse education; a new program Califano is purshing to deal with teen-age pregnancy; a new "global perspective? Program Education Commissioner Boyer is pushing, and the teacher Corp.

The proposal for a Cabinet-level education department was praised last night by John Ryor, president of the National Education Association, which has lobbied for such a department since 1922.

A department would, he said, permit better use of federal dollars for education, help the development for the first time, "a coherent national education policy, and "make certain that education is clearly delineated as a top national priority.