Cognitive radio enabled small cell network is an emerging technology to address the exponential increase of mobile traffic demand in the next generation mobile communications. Recently, many technological issues such as resource allocation and interference mitigation pertaining to cognitive small cell network have been studied, but most studies focus on maximizing spectral efficiency. Different from the existing works, we investigate the power control and sensing time optimization problem in a cognitive small cell network, where the cross-tier interference mitigation, imperfect hybrid spectrum sensing, and energy efficiency are considered. The optimization of energy efficient sensing time and power allocation is formulated as a nonconvex optimization problem. We solve the proposed problem in an asymptotically optimal manner. An iterative power control algorithm and a near optimal sensing time scheme are developed by considering imperfect hybrid spectrum sensing, cross-tier interference mitigation, minimum data rate requirement and energy efficiency. Simulation results are presented to verify the effectiveness of the proposed algorithms for energy efficient resource allocation in the cognitive small cell network.