Carroll scored one and was controversially denied another in the defeat to Chelsea.
"We have been happy with what big Andy has done since he came to Liverpool," said the Scot.
"If the ones who were critical of him are going to be fair and honest, they might have to re-write their pieces.
"If they don't want to do that, fine. It's not my problem.
"It doesn't change our opinion. He came on and lifted the team. He got the goal and was unlucky not to get another one."