In this paper, we consider the performance of coded wireless communication systems experiencing non-frequency selective fading channels in shadowed environments. The quality of service (QoS) in a wireless network is dependent on the packet error outage (PEO). We address the problem of finding a tractable expression for the coded PEO over Nakagami-m channels with shadowing, considering multilevel modulations, various block and convolutional channel coding schemes and hard decision decoding. In order to obtain the coded PEO, an inversion of the coded packet error probability (PEP) w.r.t. the signal to noise ratio (SNR) is needed. To this end, we propose an invertible approximation for the coded PEP w.r.t. the uncoded bit error probability (BEP) in Nakagami-m fading channels which is accurate for all BEPs of interest. The BEP itself depends on the average SNR and we hence make use of previous results on the inversion of the uncoded BEP w.r.t. the SNR in Nakagami-m fading channels, holding for M-PSK and M-QAM signals. We were thus able to obtain a reliable closed form expression for the coded PEO in flat fading and shadowing channels. The theoretical findings are verified by means of simulations.