What Japanese phrase can I use to report something lost?
"~o wasuremashita/nakushimashita" ("I left/lost ~") gets the situation across. Tell station staff if it's on a train, tell the shop if it's inside a store, and go to a koban police box if you're not sure or think it may have been stolen.
Japan has a strong culture of returning lost items, and a surprising number turn up at stations and koban — it's worth checking before giving up hope.
For the judgment call on exactly who to contact — station, police, or shop — see the separate article on lost items and who to call.
Reporting something lost
電車に忘れ物をしました。/財布をなくしました。
Densha ni wasuremono o shimashita. / Saifu o nakushimashita.
I left something on the train. / I lost my wallet.