Flower saw red as early as the second minute after punching Lance Hohaia twice in quick succession as Wigan were forced to play 78 minutes with 12 men.
Speaking to Sky Sports News, Wane admitted that the prop made a "huge error" and refused to defend the 26-year-old.
"I'm not going to try to [defend Flower]. It's a red; he's punched him in the head and deserved to go," he said.
"He's devastated. He's made a huge error today but we just move on, we're all in it together. I've made mistakes and he's made one today."