The chief rabbi spoke of the Jewish community's "duty of remembrance" at a service to mark Israel's Holocaust Memorial Day.
Lord Sacks, who held a question and answer session with Jewish teenagers at JFS School before the annual commemoration, was one of several speakers at the event.
More than 800 people were at the Kenton school to hear performances by Chazan Jonny Turgel and the Shabbaton Choir, readings by pupils and testimony from survivor Alec Ward.
Mr Ward spoke of his youth surviving in the ghetto and smuggling to keep his family alive.
Lord Sacks said: "As a Jewish people we share a collective faith as well as a collective fate. Nowhere in our history was this more evident than during the Shoah. As such, the Shoah has become a core and defining aspect of our collective memory.
"Every Jew, wherever they live in the world, however religious they are, is in some sense a survivor, and therefore the duty of remembrance is one which falls on all of our shoulders," he added. "It is only by remembering the darkness of the past that we can hope to bring light into our world, for the sake of this generation and generations not yet born."
Daniel Taub, the Israeli ambassador to the UK, marking his first Yom Ha'Shoah in the post, spoke of the need for every Jew "to become a witness" to the Holocaust.
JFS head teacher Jonathan Miller said it was an honour for the school to host the service. "The essential message, to pass on the memory of these tragic events, was conveyed in a powerful and effective way."