The IEEE 802.15.4 standard is considered as the most notorious MAC layer for Wireless Sensor Networks (WSNs) in both single hop and multi-hop contexts. For instance, in a multi-hop environment, the unslotted IEEE 802.15.4 is adopted as the medium access scheme. Several works evaluated the performance of the unslotted IEEE 802.15.4 in terms of average delay, exact average energy consumption, reliability, etc. But, none of the existing studies derived analytical energy consumption bounds of this MAC layer. In this paper, we propose an energy consumption analysis of the unslotted CSMA/CA based on a discrete Markov chain modeling of the backoff process. Therefore, we derive approximated average energy consumption and energy consumption bounds of beaconless IEEE 802.15.4. The probabilistic energy consumption bounds are computed based on generalized transition state diagrams. The bounds are expressed as a function of the probability that a packet energy consumption exceeds a certain value. Finally, we validate the analytical results by simulation using the Omnet simulator.