  Neutrino (antineutrino) scattering off $^{12}$C is one of various important
key reactions for $\nu$-process in the nucleosysnthesis of light nuclei. Most
of neutrino-nucleus scattering are considered through indirect processes within
the energy range from a few to tens of MeV. Target nuclei are excited by
incident neutrino (antineutrino) through various transitions, and subsequently
decay into other nuclei with emitting particles. But, direct processes are also
feasible, in which incident neutrino (antineutrino) strips directly one nucleon
from target nuclei. Consequently, direct processes may affect abundances of
$^{11}$C and $^{11}$B additionally to indirect processes. We investigate direct
neutrino (antineutrino) quasi-elastic scattering off $^{12}$C around the energy
region liberating one nucleon and discuss implications of direct processes in
the nucleosynthesis. The direct processes might be comparable to the indirect
processes if the final state interaction is taken into account.
