In this paper, wireless systems operating under queueing constraints in the form of limitations on the buffer violation probabilities are considered. The throughput of wireless systems operating under such constraints is captured by the effective capacity formulation. It is assumed that finite blocklength codes are employed for transmission. Under this assumption, a recent result on the channel coding rate in the finite blocklength regime is incorporated into the analysis and the throughput achieved with such codes in the presence of queueing constraints is identified. Interactions between the effective rate, queueing constraints, error probabilities, and blocklength values are investigated. In particular, it is shown that for given signal-to-noise ratio, blocklength, and quality of service exponent, the effective rate is maximized at a unique decoding error probability value.