We consider the ℋ_∞ almost output synchronization and regulated output synchronization problem for heterogeneous directed networks with external disturbances where agents are introspective (i.e. agents have access to a part of their own state). A decentralized protocol is designed for each agent, without exchanging internal controller states with neighboring agents, to achieve output synchronization and regulation while holding back the ℋ_∞ norm from the disturbances to the synchronization errors in the closed-loop transfer function of the network. The method is illustrated by simulation examples.