The Douwd was able to create elaborate "illusions" of people and objects. These illusions resembled holodeck projections, since they could interact with physical objects and energy. One of his most impressive illusions was a massive starship capable of effortlessly withstanding the firepower of the Enterprise-D and overwhelming the Enterprise's shields with its own weapon bursts. He was able to sustain this illusion while it flew away from Rana IV at high warp for several minutes.
The Douwd was also able to disguise himself as a human, move rapidly in an intangible state, and create a debilitating musical pattern in the mind of Deanna Troi to distract her. He claimed that he had exterminated the entire Husnock race with a single thought.
The Douwd claimed to be unable to disguise his true nature from Deanna (hence the need to distract her). He was apparently unable to keep constant track of the activities of the Enterprise in orbit over the planet. Presumably, controlling the minds and memories of everyone on the Enterprise so they would leave immediately was beyond his abilities.
Disguises and False Surroundings
Everything that the Douwd told Picard and other members of the Enterprise crew is suspect. He claimed to have lived in disguise among humans for decades as Kevin Uxbridge, having fallen in love with a woman named Rishon while visiting Earth. He later moved to the Rana IV colony with her. The colony came under attack by the alien Husnock, whom he destroyed completely in a fit of rage after Rishon died fighting them. He then created an autonomous illusion of Rishon, with whom he intended to continue living on Rana IV, assuaging his own grief and guilt.
Little, if any, of the Douwd's story can be confirmed. There is no independent evidence that the Husnock ever existed, let alone that they attacked the Rana IV colony or that he subsequently exterminated them. It is impossible to determine whether he lived for decades as Kevin Uxbridge or simply assumed the name of one of the dead colonists when the Enterprise arrived.
The only thing truly known is that the Douwd got what he appeared to want; the Enterprise left him alone on Rana IV.