  The experimental searches for diffuse supernova neutrino background and
proton decay in next-generation large liquid-scintillator (LS) detectors are
competitive with and complementary to those in the water-Cherenkov detectors.
In this paper, we carry out a systematic study of the dominant background
induced by atmospheric neutrinos via their neutral-current (NC) interactions
with the $^{12}{\rm C}$ nuclei in the LS detectors. The atmospheric neutrino
fluxes at the location of Jiangmen Underground Neutrino Observatory (JUNO) are
used, as the JUNO detector is obviously a suitable representative for future LS
detectors. Then, we implement the sophisticated generators \texttt{GENIE} and
\texttt{NuWro} to simulate the neutrino interactions with the carbon nuclei,
and the package \texttt{TALYS} to deal with the deexcitations of final-state
nuclei. Finally, the event rates for the production of additional nucleons,
$\gamma$'s, $\alpha$'s, pions and kaons are obtained and categorized, and the
systematic uncertainty of the NC background represented by a variety of
data-driven nuclear models is estimated. The implications of the NC background
from atmospheric neutrinos for the detection of diffuse supernova neutrino
background and proton decay are also discussed.
