United Nations Ambassador Jeane J. Kirkpatrick said today that the United States had "behaved like a bunch of amateurs" in the U.N. and that this country has "been virtually powerless for more than a decade."

Wrangling with Secretary of State Alexander M. Haig Jr. in past months, Kirkpatrick, in a luncheon talk at the Union League Club, took care to stress that she was not singling out the current administration for blame. The "impotence" and "ineptitude," she said, "has persisted through several decades, several administrations" and "does not represent worldwide revulsion against the Reagan administration or even myself."

Nonetheless, she said, "the decline of U.S. influence in the U.N. is part and parcel of the decline of U.S. influence in the world . . . and that is a direct reflection of what has been a persisting U.S. ineptitude in international relations.

" . . . We have not been effective in projecting a conception of international programs; we have not been good at the politics of the United Nations. It is a political arena . . . . We have treated it as though it were something other than a political arena . . . a strange thing, really."

She recommended that the United States, in an effort to improve its workings within the U.N., "ought to have a permanent representative who'll stay there long enough to come to know the scene."

She added, "I hate to say that. It makes it sound like I'm making an application for a long tenure. I couldn't stand it, believe me."