In one of the "Hitchhiker's Guide to the Galaxy" books by Douglas Adams, we're introduced to an execution machine. The victim hooked into this machine is able to see the universe- all of it- in its vastness and splendor. He witnesses every galaxy, and the vast emptiness between them. Finally, after the scope of all this is appreciated by him, he notices something in the most insignificant area of the vast splendor before him. In tiny-the most microscopic of microscopic- font, is a little arrow, with the words "you are here" written next to it.
The victim's brain then melts at the realization of how utterly small and insignificant they truly are.
I bring this random point up because I feel this one-off joke from a British comedy writer best exemplifies the source of horror for most Lovecraft stories. Saying it's about evil is selling it short. It's about how human morality is as insignificant as humans themselves.
The destruction of the human race by the forces portrayed in the stories isn't their goal, or even a sacrifice they're willing to make. It's an after-effect so utterly tiny and insignificant to them that they spare it no thought whatsoever. No more than you consider the fate of the microbes you crush when you walk from one room to another in your house.
The sobering realization of how small and unimportant we are was very effective horror for older generations. Part of the reason for this was that past generations were far more religious, on average, than the current one. One of the big tenets of man-made religions is how awesome and special humans are, after all. "God created the entire universe JUST to make us! We're the creator's pet, the most important things in all the cosmos!" is a pretty common sentiment.
Thus, seeing a scenario where, not only are we NOT important, but so far beneath contempt that the instruments of our destruction lack so much as an evil desire to see us destroyed, would be a pretty effective tool of horror.
Naturally, whether that is still horrifying in a modern context depends a lot on the person reading it. Most of the works Lovecraft is most famous for didn't really scare me, personally, but I appreciated their breadth of scope. I'm ashamed to admit that the one Lovecraft story that did scare me did so more with a "wham-line" than any sort of deep philosophy:
"YOU FOOL, WARREN IS DEAD!"
A line about as horrifically 'deep' and 'thoughtful' as "The call was coming from INSIDE THE HOUSE!"... but alas, I'm easy to fright.