Miliband said the British government reiterated its call for the "immediate safe release of all the remaining hostages".
"Hostage-taking is never justified in any cause. Today's terrible news underlines the gravity of the crimes associated with it," he said.
The bodies were handed over to officials on Friday.
The group which kidnapped the five men had sent a video featuring one of the captives to the British embassy in Baghdad, the British foreign ministry said in March.
Britain's Channel 4 News said the video showed Moore saying the group was being treated well.
More than a year earlier, another video featuring Moore had been aired by Dubai-based Al Arabiya television, in which he called on Gordon Brown, the British prime minister, to free nine Iraqis in return for their freedom.
The group had previously demanded that Britain withdraw its troops from Iraq.
In a video released in July, the group claimed that one of the men had committed suicide, but this has not been confirmed.