"The medal is for all of Israel, for everyone who supported me and cheered me on.
"I'm waiting for someone to wake me up. I gave my soul and it paid off. Whoever said you can't succeed in Israel, is wrong."
Gerbi is the second Jewish medallist in Brazil following in the footsteps of American swimmer Anthony Ervin who won gold in the 4x100m Medley Relay.
Gerbi's bronze was Israel's eigth in Olympic history, four of which have come in judo.
Former team-mate Alice Schlesinger, now competing for Team GB, suffered a disappointing defeat in the second round of the same competition.
Dudi Sela's run in the Men's Singles tennis competition ended in the second round as he went down 6-3, 6-3 to David Goffin of Belgium.