"What people forget about children's performances is that children will know when you're talking down to them. They will know when they're not getting the very best," observed New York City Ballet star Jacques d'Amboise.

The Kennedy Center's two-week festival for children concluded yesterday-leaving center officials understandably pleased. After a 1977 premiere festival that was "frankly exploratory" and a 1978 series that was an "improvement" but still "a learning experience," "this year, it really has come of age," says director of operations Thomas R. Kendrick, who oversees the project.

The key to the center's accomplishment was its adherence to d'Amboise's injunction. The very best was offered in such varied programs as the two-story theater performances by groups from Atlanta and Grand Rapids, Mich.; the slick tribute to Duke Ellington organized by singer Leon Bibb and jazz pianist Stan Keen; the Kabuku retelling of "Sleeping Beauty" from Albany; a children's work from the New York City Opera Theater, and d'Amboise's own program of ballet, which managed to be both down to earth and sophisticated at the same time. The latter and the Ellington program were special commissions by the Center, and will be the foundation of similar festivals in Chicago and Seattle.

No other cultural center now produces a more ambitious a children's festival, quite aside from the question of level of achievement. This year about 25,000 children and adults attended about 50 free performances.

Superior achievements requires overcoming the almost universal tendency by performers, producers and performing arts institutions to relegate children's activities to token "arts appreciation" status-low budget and deputized to the second term. Also to be avoided are the gags and cliches of much children's television. Despite exceptions like Leonard Bernstein's Young People's Concerts with the New York Philharmonic, mediocrity has prevailed. "Our biggest problem is the trouble we have getting top talent interested," says Carole Huggins, the Center's assistant education director for its Programs for Children and Youth.

D'Amboise's is not the Center's first recruit from the big leagues. Last year Sarah Caldwell brought her Opera New England in composer Lucas Foss' operatic adaptation of Mark Twain's short story, "The Jumping Frog of Calaveras County."

Now Gian Carlo Menotti has been commissioned to compose "a dance-opera piece, hopefully for next year," according to education director Jack Kukuk. "He's been given a general concept and it's up to him to come up with a specific subject." The cost for the Center is expected to be about $20,000.

A further benefit of attracting the Caldwells and the d'Amboises is that the overall quality of offerings is raised. "Getting people at that level leads other people at the level to participate," says Huggins. "We are getting more contacts; competition is getting tougher and tougher and there is more willingness, especially for corporate support."

Another essential has been the agreement of star performers to work for practically nothing. If d'Amboise, City Ballet ballerina Kay Mazzo, and the numerous other dancers in his program had charged standard fees, costs would have greatly exceeded the $30,000 budget.

Even so there are still expenses. Kukuk notes that "last year Sarah Caldwell donated her time, but we still had to pay for her musicians." He said the festival this year cost in excess of $100,000, though exact expenses are unclear because of the multiplicity of sources for the individual productions.

The children's festival, which carries the title "Imagination Celebration," is an undertaking of the Center's Programs for Children and Youth, all of whose projects are free and are financed by a budget of about $350,000. Two-thirds of that money comes from the Center's corporate fund.

Other programs include children's arts series at the Center (now including five productions) in both the fall and the spring. This spring's shows ended in late March. Also there is a school residency series, some starting tomorrow, during which five separate productions will visit area schools over the next three weeks. Productions, as well as attendance at the Center, are apportioned according to size among 12 area school systems, including parochial schools. In addition, the branch for Children and Youth conducts teacher workshops to supplement the activites and provides training aids.

These projects constitute part of the educational division, now a $1.5 million a year enterprise that was still in an embryonic stage when Kukuk came to the Center about three years after its 1971 opening. Other subdivisions of it are the American College Theater Festival and the large Alliance for Arts Education, which provides financial aid and technical assistance now to 40 states in developing local arts education programs.

The Education Division's activities are also directly tied to those of the National Committee, Arts for the Handicapped, which held its national convention at the Center to coincide with the festival. The NCAH bore part of the d'Amboise program's cost. These two groups have overlapping staffs.

This year the festival has an appropriate home-the new Terrace Theater. In both size and ambiance the Theater seems almost ideal for the scale of such programs. Earlier they were presented in either the Eisenhower Theater, the Grand foyer or in the tent outside-all of which were either too large, too awkward or both.

"Intimacy is one of the keys to direct communication to children's audiences," says John Donahue, whose Minneapolis Children's Theater is described by Huggins sthe "citadel" of such undertakings in this country. It is the only major children's theater that has both a year-round schedule and its own house of 735 in which to perform. CAPTION: Pictures 1 and 2, From the Kennedy Center's "Imagination Celebration 1979" for children, a down-to-earth "Encounter With Dance" (above) and a Kabuki retelling of "Sleeping Beauty."