We have used atomistic molecular simulations to study the effect of nanofiller dispersion on the glass transition behavior of cross-linked epoxy-carbon nanotube (CNT) nanocomposites. Specific chemical interactions at the interface of CNTs and cross-linked epoxy create an interphase region, whose impact on the properties of their nanocomposites increases with an increasing extent of dispersion. To investigate this aspect, we have compared the volumetric, structural, and dynamical properties of three systems: neat cross-linked epoxy, cross-linked epoxy nanocomposite containing dispersed CNTs, and cross-linked epoxy nanocomposite containing aggregated CNTs. We find that the nanocomposite containing dispersed CNTs shows a depression in the glass transition temperature (T-g) by similar to 66 K as compared to the neat cross-linked epoxy, whereas such a large depression is absent in the nanocomposite containing aggregated CNTs. Our results suggest that the poor interfacial interactions between the CNTs and the cross-linked epoxy matrix lead to a more compressible interphase region between the CNTs and the bulk matrix. An analysis of the resulting dynamic heterogeneity shows that the probability of percolation of immobile domains becomes unity near the T-g calculated from volumetric properties. Our observations also lend support to the conceptual analogy between polymer nanocomposites and the nanoconfinement of polymer thin films.