Space-time block coding (STBC) provides substantial diversity advantages with a low decoding complexity. However, these codes are not designed to achieve coding gains. Outer codes should be concatenated with STBC to provide additional coding gain. In this paper, we analyze the performance of concatenated trellis-coded STBC schemes over shadowed Rician frequency-flat fading channels. We derive an exact pairwise error probability (PEP) expression that reveals the dominant factors affecting performance. Based on the derived PEP, in conjunction with the transfer function technique, we also present upper bounds on the bit error rate (BER), which are further shown to be tight through a Monte-Carlo simulation study.