Green communications have emerged as a demanding concept for improving the network energy efficiency (EE). In this paper, a pricing-based approach is investigated to achieve energy-efficient power allocation in relay-assisted multiuser networks. We introduce a network price to the power consumption as a penalty for the achievable sum rate, and study its impact on the tradeoff between the EE and the spectral efficiency (SE). It is hard to directly solve the problem as it is non-convex, and thus a concave lower bound on the pricing-based utility is applied to transform the problem into a convex one. Through dual decomposition, a $q$-price algorithm is proposed for iteratively tightening the lower bound and finding the optimal solution. In addition, an optimal price that enables green power allocation is defined and found from the viewpoint of maximizing EE. We further analyze the optimal power allocation strategies of the pricing-based approach in a two-user case under different noise operating regimes, yielding on-off, water-filling, and channel-reversal approaches, etc. Finally, the performance of the proposed approach is evaluated by computer simulations, and we characterize the interaction between the EE and SE for various network parameters when the network is designed from the energy-efficient perspective.