If you are slightly mis-remembering some of the publication information (not a Twilight Zone anthology, but possibly one of Harlan Ellison's collections, like Shatterday, the 1980 title story of which was made into a Twilight Zone episode) you might well be remembering How's the Night Life on Cissalda?.
The main character is part of an experiment that involves shifting to another universe, and, when he comes back, he is doing.. well. here; the opening line:
When they unscrewed the time capsule, preparatory to helping temponaut Enoch Mirren to disembark, they found him doing a disgusting thing with a disgusting thing.
The creature turns out to be the perfect sexual partner for almost any being on earth... Again, to quote:
“It’s both, and neither,” said the expert from Johns Hopkins. “It seems equipped to handle anything up to and including chickens or kangaroos with double vaginas.
In the end, they do manage to separate our hero from his... err.. companion.. and that doesn't go well for him; the creatures are telepathic and don't take rejection well.. so he can never mate with another one.
Eventually, the creature communicates home, and it's species comes to visit:
Now, in mere moments, the flood of teleporting Cissaldans overflowed the Earth: one for every man, woman and child on the planet. Also leftovers for chickens and kangaroos with double vaginas.
This results in the eventual extinction of most life on earth, as no one is willing to stop, not even to eat, reproduce, or any of the other tasks required to keep life going.
Our hero, however, unable to enjoy a Cissaldan again, ends up being the last human alive, and speculates on what creatures will follow man. Possibly cockroaches, although he hopes not.
It ends on him having a bittersweet thought about the whole situation.
He was smiling sadly. It had just occurred to him that his only consolation in bearing the knowledge that he had destroyed the human race was that for a little while, in the eyes of the best fuck in the universe, he had been the best fuck in the universe.
There wasn’t a cockroach in the world who could claim the same.