Woods, in conjunction with team-mate Ben Hunt, accidentally picked up Mannah in the tackle and he was placed on report by referee James Child.
He has escaped a ban though after the World Cup panel agreed with him when he said he did all he could to ensure the tackle was not dangerous.
"I knew when I did it that it was going into an awkward situation, so I tried to pull him back," Woods said.
"That's why he didn't land on his neck or his shoulder. I tried my best. I got caught in a bad situation. I won't be pulling any legs any time soon. It didn't look good when they did the slow motion on the camera."