Oates, 32, beat Slovenian Adrian Gomboc in the semi-finals but came up short against Margvelashvili in the final.
Fellow Briton Nekoda Davis, 22, lost to Nora Gjakova of Kosova in the -57kg bronze-medal match.
Ashley McKenzie, 26, lost to eventual champion Walide Khyar of France in round two of the men's -60kg.
Britain's Colin Oates took -66kg silver at the European Judo Championships after defeat by Georgia's Vazha Margvelashvili in Kazan, Russia.