A no-reference (NR) method based on an artificial neural network (ANN) approach is proposed in this paper to estimate the objective quality of video-plus-depth streams subject to packet loss in depth data. A novel aspect of this method is the use of information only taken from packet headers, up to the network abstraction layer (NAL), requiring a very low complexity parsing of the compressed video streams. A maximum of seven packet-layer parameters were found to be enough to provide accurate objective quality estimates given by the structural similarity index (SSIM). The accuracy of the quality estimates, evaluated by comparison with the actual SSIM quality scores, is shown to be sufficiently high (e.g., Pearson Linear Correlation Coefficient over 0.92) for lightweight implementations of 3D video quality monitors at end-user receivers and also at network nodes.