A carbon responsibility allocation method based on the complex structure carbon emission flow theory is proposed to address the problem posed by the unclear carbon responsibility allocation of each link in the low-carbon development of electric power. First, the calculation method, distribution characteristics, and mechanism of carbon emission flow were analyzed. The “carbon potential of complex structure” concept was introduced to track “carbon trajectory” and “green trajectory” by harnessing the ability of complex structures to retain two-dimensional information. Subsequently, the carbon responsibility allocation methods for network loss and users’ electricity consumption behavior were developed to realize the accurate carbon responsibility allocation of each system link. Finally, the effectiveness and advancement of the proposed carbon responsibility allocation method were verified using the improved IEEE 6-bus and 30-bus test systems. The application of the proposed complex structure carbon potential in the carbon emission flow theory expands the research dimension of electric power carbon emission for low-carbon development from the “carbon perspective,” provides a novel optimization space for the operation of the distribution network and realizes the carbon emission flow theory, which serves as a bridge from calculation evaluation to optimization decision.