  Recently, the BESIII collaboration performed a precise measurement of the
$e^+e^-\to \eta J/\psi$ cross section. It is puzzling that the resonance
parameters of the reported $Y(4230)$ show a substantial divergence from the
previously measured results in both the open-charmed and hidden-charmed decay
channels, and the line shape asymmetry of the data approaching 4.2 GeV also
suggests that it might be difficult to characterize the details of the
structure around 4.2 GeV by a single resonance. This has motivated our great
curiosity about how the charmonium states are distributed in the measured
energy range and how they shape the puzzling data of the $e^+e^-\to \eta
J/\psi$ cross section. In this work, we use five theoretically constructed
charmonia in the range of $4.0\rm{-}4.5$ $\text{GeV}$, i.e., $\psi(4040)$,
$\psi(4160)$, $\psi(4220)$, $\psi(4380)$, and $\psi(4415)$, to apply a combined
fit to the data, in which their calculated decay ratios into $\eta J/\psi$ via
hadronic loop mechanism are taken as input. The fit results can reproduce the
measured cross section data well, especially for the subtle line shape around
4.2 GeV, showing that the structure around 4.2 GeV is possible from the
contribution of both $\psi(4160)$ and $\psi(4220)$.
