  By measuring the THz electron spin resonance (ESR) transmission spectra and
high-field magnetization on the spin-gapped system CuTe$_2$O$_5$, we identified
the singlet-triplet excitations in the dimerized non-magnetic ground state. The
determined spin-gap value of $h\nu_0=4.94$ meV at the $\Gamma$ point
($\mathbf{Q}\simeq\mathbf{0}$) is significantly smaller than the strongest
antiferromagnetic exchange interaction between the Cu ions predicted by
theoretical investigations. We also observed the critical field
$H_{c1}^{a^*}=37.6$ T for \textbf{H} $\bot$ \emph{bc}-plane and
$H_{c1}^{bc}=40.6$ T for \textbf{H} $\|$ \emph{bc}-plane at the onset of
non-zero magnetization, consistent with the gap value and corresponding
anisotropic \emph{g}-factors determined previously. The observed
singlet-triplet excitations in Faraday and Voigt configurations suggest a
mixing of the singlet state with the $S_z=0$ triplet state and the $S_z=\pm 1$
triplet states, respectively, due to the Dzyaloshinskii-Moriya (DM) interaction
with a DM vector perpendicular to the crystalline \emph{bc}-plane.
