Japan's Foreign Minister said today that his country was ''seriously concerned'' about the loss of a hydrogen bomb off Okinawa 24 years ago, and said Japan would press for ''full details'' about the incident from the United States. The comments by the official, Sosuke Uno, came after the Government was sharply criticized both by the Japanese press and by some civic and anti-nuclear groups for playing down reports that the lost bomb is still under the ocean 80 miles from a Japanese island. Over the last two days the Pentagon has provided the first details of the 1965 accident, admitting for the first time that the accident happened off Japan's shores rather than 500 miles from land, as it originally contended. The aircraft carrier Ticonderoga, which was carrying the weapon when it was lost overboard with an A-4 aircraft, was reportedly heading to Yokosuka, the naval base south of Tokyo, from Vietnam. This morning the Asahi Shimbun, the most liberal of Japan's major dailies, castigated the Japanese Foreign Ministry for ignoring the first reports of the accident. In an editorial, the newspaper said that ''an unexpectedly profound gap'' exists between ''the people's feelings'' about the presence of nuclear weapons and the Government's willingness to ignore the presence of the weapons in the interest of avoiding strains with the United States.