In order to understand the physical properties of the series of organic conductors $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]$X$ with $X$ = Cl, Br, and I, not only electronic correlations but also the effect of disorder has to be taken into account. While for Cl- and Br-containing salts the influence of both parameters were investigated and a universal phase diagram was proposed, the position of $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]I is still not settled. Here we have conducted transport, infrared, and dielectric measurements on single crystals of the title compound to clarify its electronic state at low temperatures. The correlation strength was determined as $U/W \approx 2.2$; thus this salt is placed deeper in an insulating state compare to the two sister compounds. We found that inherent disorder leads to a Coulomb localized insulating state similar to the moderately x-ray-irradiated $\kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Cl.