$1/N^2$ corrections to deep inelastic scattering (DIS) of charged leptons from glueballs at strong coupling are investigated in the framework of the gauge/gravity duality. The structure functions $F_1$ and $F_2$ (and also $F_L$) are studied at subleading order in the $1/N^2$ expansion, in terms of $q^2$ and the Bjorken parameter $x$. The relevant type IIB supergravity one-loop diagrams (which correspond to DIS with two-hadron final states) are studied in detail, while $n$-loop diagrams (corresponding to DIS with (n+1)-hadron final states) are briefly discussed. The $1/N^{2n}$ and $\Lambda^2$/$q^2$ dependence of the structure functions is analyzed. Within this context two very different limits are considered: one is the large $N$ limit and the other one is when the virtual photon momentum transfer q is much larger than the infrared confining scale $Λ$. These limits do not commute.