It is now generally accepted that even low amounts of quenched disorder disrupt long-range order in anisotropic systems with continuous symmetry. However, very little is known on the key item of the nature of the residual order, if any, and particularly if this has quasi-long-range or truly-short-range character. Here we address this problem both experimentally for the nematic 6CB in dilute aerosils and with computer simulations. We find that the residual order is short ranged and scales with disorder density in agreement with the Imry-Ma argument.