Device-to-device (D2D) communication, where user equipments (UEs) in proximity communicate directly with each other, is an alternative technology for densification in future wireless communications featuring extremely dense and heterogeneous networks. The intrinsic characteristics of D2D communication include (1) limited energy capacity of battery powered UEs, (2) necessary power consumption to maintain D2D communication connections, and (3) desired quality of service (QoS) on the D2D communication to ensure performance of upper layer applications. These make it one of the most challenging issues in D2D communication, which is how to achieve the best power-QoS tradeoff. The aim of this paper is to provide results that shed light on this issue, by establishing relations between the transmission power and the QoS requirements. In particular, we present closed form expressions for transmission power allocation to meet QoS requirements under D2D communication with Rayleigh channel. Numerical and simulation results illustrating the insights are also provided and discussed.