President Carter's afternoon at the opera Sunday created a minor furor at the White House yesterday and a warning to expect future attempts by the President to sneak off for "family and personal reasons" without the company of reporters.

Carter, his wife, Rosalynn, and daughter, Amy, took off unannounced Sunday for the Kennedy Center and a performance of "Madame Butterfly" by the Washington Opera Society.

Led by correspondents for the television networks and the wire services, some reporters protested yesterday that they were not notified of this and were misled when they asked about it.Specifically, they said representatives of the Secret Service, the Army Signal Corps and the Executive Protective Service told them Carter was in the White House when, in fact, he was at the Kennedy Center.

White House press secretary Jody Powell apologized for any misleading statements, which he said resulted from a "misunderstanding" by White House employees "overzealously interpreting" the President's instructions not to announce the trip.

But, Powell warned, "the President does wish to reserve the right to go places for strictly family or personal reasons without prior announcement . . . The President has a right to go to the opera without prior public knowledge."

In response to a question, Powell left open the possibility that Carter might attempt to leave Washington on what he considered private business without the huge press corp that usually follows him everywhere. "If he chooses to go somewhere without public notice," Powell said, "I don't know of any law or tradition or natural or divine precept that would prevent it."

The press secretary noted that during the pre-inaugural period Carter often moved around his hometown of Plains, Ga., unannounced. He predicted that such instances when Carter is President would be "fairly rare."

Asked if the President had ever thought of attempting to slip away from his ever-present cadre of Secret Service agents, Powell said, "I don't know. It would be an interesting experiment.