What to do in the first few hours after realizing it's gone.
Report it to local police first to get an official record, then contact your embassy or consulate, which can typically issue an emergency travel document faster than you'd expect. Keep a photo of your passport's information page saved separately, since it speeds up the replacement process considerably.
If you were relying on your passport alongside your license and IDP for identification at a rental counter, contact the rental company as well, since they may need updated documentation before you can continue driving.