The Washington press corps has been "reasonably balanced and fair" in its coverage of the Reagan administration, White House communications director David Gergen told a group of 75 journalists at the Hotel Washington last night. But he also told the Washington Press Club symposium on White House coverage that recently relations have been strained, complaining of two major shortcomings:

* "Too great a tendency to concentrate on the trivial" and not on "deeper issues." Gergen cited news stories last August about White House advisers failing to wake President Reagan when Libyan fighter planes were shot down in the Mediterranean, criticizing them for "little historical perspective" and saying that "president after president has slept through" similar events.

* A focus "more on process than on policy" and too much emphasis on "the personality of who's in charge" rather than substantive issues. Profiles and process make "better stories" he said, are "easier" to write and "sell more papers." Gergen pointed to stories about the relationship between Federal Reserve Chairman Paul Volcker's and the president, suggesting that monetary policy itself receives scant attention. In later questioning, Gergen said that in the "tendency to lunge for the headline of the day," there is a "lack of focus on policy . . . Washington doesn't have to revolve around the front page of the Style section."

Gergen said that the White House has "tried to achieve better relations" with the press and that there is "no anti-press campaign in this administration."

A panel of White House correspondents responded. Sara Fritz of U.S. News and World Report said she detects an "anti-press attitude" in the administration, citing attacks on the Freedom of Information Act and increasingly limited access to the president. She also said "the White House tends to blame the press for problems they created."

Ann Devroy of Gannett asked Gergen, "Do you think it was fair to scare half the country about Libyan hit squads" and then provide no subsequent explanation? He replied that although the White House has been accused of "orchestrating" the issue, "we didn't want that story out there."

Carl Luebsdorf of the Dallas Morning News responded to the "triviality" issue by saying "the episodic is important." Luebsdorf said the Libyan event was telling because it demonstrated the president's detachment and "well known" policy of delegating responsibility. Other panelists were John Margolis of the Chicago Tribune and moderator Miles Benson of Newhouse.