Context. The Carina Nebula represents one of the largest and most active star forming regions known in our Galaxy. It contains numerous very massive (M > ∼ 40 M ) stars that strongly affect the surrounding clouds by their ionizing radiation and stellar winds. Aims. Our recently obtained Herschel PACS and SPIRE far-infrared maps cover the full area (≈8.7 deg 2 ) of the Carina Nebula complex (CNC) and reveal the population of deeply embedded young stellar objects (YSOs), most of which are not yet visible in the mid-or near-infrared. Methods. We study the properties of the 642 objects that are independently detected as point-like sources in at least two of the five Herschel bands. For those objects that can be identified with apparently single Spitzer counterparts, we use radiative transfer models to derive information about the basic stellar and circumstellar parameters. Results. We find that about 75% of the Herschel-detected YSOs are Class 0 protostars. The luminosities of the Herschel-detected YSOs with SED fits are restricted to values of ≤5400 L , their masses (estimated from the radiative transfer modeling) range from ≈1 M to ≈10 M . Taking the observational limits into account and extrapolating the observed number of Herschel-detected protostars over the stellar initial mass function suggest that the star formation rate of the CNC is ∼0.017 M /year. The spatial distribution of the Herschel YSO candidates is highly inhomogeneous and does not follow the distribution of cloud mass. Rather, most Herschel YSO candidates are found at the irradiated edges of clouds and pillars. The far-infrared fluxes of the famous object η Car are about a factor of two lower than expected from observations with the Infrared Space Observatory obtained 15 years ago; this difference may be a consequence of dynamical changes in the circumstellar dust in the Homunculus Nebula around η Car. Conclusions. The currently ongoing star formation process forms only low-mass and intermediate-mass stars, but no massive (M > ∼ 20 M ) stars. The characteristic spatial configuration of the YSOs provides support to the picture that the formation of this latest stellar generation is triggered by the advancing ionization fronts.