The lack of motility in a prosthetic eye can trigger unnaturalness in observers who interact with its user, mainly owing to the asynchronization in the movements of the prosthetic and unaffected eyes. For people using prosthetic eye, this is a crucial concern in addition to the aesthetic nature and immobility of the prosthesis. To address this limitation, it is crucial to realize artificial eye in conjunction with the unaffected eyeball, although some delays are expected regardless. However, inherent delays in actuator response and control in mechanical approaches render this objective unattainable. To obtain design standards for prosthetic eyes that facilitate natural face-to-face interactions, we investigated the impact of delay in the response of prosthetic eyes on the unnaturalness perceived by observers. In the experiment, a unilateral prosthetic eye with a delay was reproduced by a 2D animation movie, participants watched movies with different time constants and dead time were varied. The results obtained from the experiment demonstrated that there is a range within which observers cannot feel unnaturalness due to delay differences in the movements between the left and right eyes, even if they notice these differences by delay. These results will contribute to realizing a better mechanically movable prosthetic eye.