I didn't find anything in interviewers with the screenwriters, but David S. Goyer is an H.P. Lovecraft fan, and others have noted an influence.
Here's a review by Goyer for an original graphic novel called Lovecraft:
"Rodionoff, Breccia and Giffen have crafted a beautiful, nightmarish homage. Reading between the lines of Lovecraft's work, they have managed to fabricate a secret history that every H.P. fan wishes were true." David S. Goyer, screenwriter of Dark City and Blade
IMDb's biography for David S. Goyer says:
He is a big fan of H.P. Lovecraft books.
Movies I Didn't Get says:
Dark City opens with darkness and the words: "In the beginning, there was nothing." The darkness is now spattered with stars and the voice of Dr. Schreber continues: "Then came the Strangers." With this opening, we are instantly reminded of the biblical book of Genesis. But the fact that there are many of them instead of one all-powerful being, the fact that they came from another dimension and that, once here, the knowledge of their existence generally drives men either to insanity or to an early grave, all give the impression that these are much older gods than the one espoused by the Christian faith. These gods, if gods they be, bear more resemblance to the ancient ones described in the horror stories of H.P. Lovecraft.
An essay called Horror in Roleplaying lists five major motives for fear that are dealt with in horror media, the last one is "Living in an Evil World":
The fear that the world, God, reality, the social order, or something else is evil, hostile, or horrible. There are good examples of horror based on questioning the entire nature of one’s reality – the movie Dark City is one, along with “cosmic” horror like H.P. Lovecraft’s writings.
Buzzy Mag says of the Dark City novel, adapted from the film:
Written by Frank Lauria, who wrote the 1977 book Communion (not to be confused with the Whitney [sic] Strieber book of the same name), the novel holds true to his trademark synthesizing of H.P. Lovecraft and Raymond Chandler (hint: the plot has a lot to do with the stealing of human souls).
(The author of the other "Communion" is in fact Whitley Strieber.)