  The IceCube (IC) collaboration recently reported the detection of TeV-PeV
extraterrestrial neutrinos whose origin is yet unknown. By the photon-neutrino
connection in $pp$ and $p\gamma$ interactions, we use the \fermi-LAT
observations to constrain the origin of the IC detected neutrinos. We find that
Galactic origins, i.e., the diffuse Galactic neutrinos due to cosmic ray (CR)
propagation in the Milky Way, and the neutrinos from the Galactic point
sources, may not produce the IC neutrino flux, thus these neutrinos should be
of extragalactic origin. Moreover, the extragalactic gamma-ray bursts (GRBs)
may not account for the IC neutrino flux, the jets of active galactic nuclei
may not produce the IC neutrino spectrum, but the starburst galaxies (SBGs) may
be promising sources. As suggested by the consistency between the IC detected
neutrino flux and the Waxman-Bahcall bound, GRBs in SBGs may be the sources of
both the ultrahigh energy, $>10^{19}$eV, CRs and the $1-100$~PeV CRs that
produce the IC detected TeV-PeV neutrinos.
