Killen told Entertainment Weekly that he does not expect another network to pick up the Jason Isaacs drama after it was axed by NBC.
"It'd be difficult given the ratings that we had to justify [a pick-up by another network]," he suggested.
The showrunner instead encouraged fans to campaign for Isaacs to receive awards recognition for his performance.
"The incredible support and enthusiasm from fans - if they wanted to use that energy for something - I would say it's better spent trying to see that Jason is recognised," he said. "That's a better campaign to wage."
Killen - who also created short-lived Fox drama Lone Star - added that he may have been "cavalier" in thinking Awake could work on network television.
"It feels like there's becoming two very distinct camps," he argued. "So I think if I show up on network again, I would bring a more network-specific idea.
"If I have ideas that feel like they belong on cable, then I think at this point, I'll probably start to take them to cable."
