The cytoskeleton underlying cell membranes may influence the dynamic organization of proteins and lipids within the bilayer by immobilizing certain transmembrane (TM) proteins and forming corrals within the membrane. Here, we present coarse-grained resolution simulations of a biologically realistic membrane model of asymmetrically organized lipids and TM proteins. We determine the effects of a model of cytoskeletal immobilization of selected membrane proteins using long time scale coarse-grained molecular dynamics simulations. By introducing compartments with varying degrees of restraints within the membrane models, we are able to reveal how compartmentalization caused by cytoskeletal immobilization leads to reduced and anomalous diffusional mobility of both proteins and lipids. This in turn results in a reduced rate of protein dimerization within the membrane and of hopping of membrane proteins between compartments. These simulations provide a molecular realization of hierarchical models often invoked to explain single-molecule imaging studies of membrane proteins.