Confinement of phantom networks of Gaussian chains between parallel surfaces is simulated through the application of a harmonic potential 1/2 Hx(2) to each chain bead at a distance x from the mean plane. We consider infinite, square (cubic) networks with a topological dimensionality of two (three), in addition to three-dimensional networks with a finite number of layers along one dimension. The partition function stays Gaussian and its integration reduces to the search of the eigenvalues of cyclic, or quasicyclic matrices. As applied to an isolated chain the confinement energy is 75% the exact value obtained by Casassa's exact approach, and the accuracy is expected to improve in the network case. At strong compressions, the confinement energy per chain epsilon(H) is about the same for all the networks, but smaller than for a single chain with the same contour length. Taking epsilon(H) in k(B)T units, M = epsilon(H)(-1) gives the number of chains in the correlation domain. Therefore, the external potential breaks up the network into smaller and smaller correlated domains, whose statistics remain unperturbed ("blobs"). The unperturbed mean-square radius of gyration reproduces previous results on the two- and the three-dimensional networks. The enormous collapse in the three-dimensional case is evidenced once again.