Gerrard has high hopes of Carroll after his end of season form for Liverpool and he did not disappoint in his first England start for 14 months.
He said: "I thought Andy did okay. It was all eyes on him because of the form he showed when he finished the season for Liverpool.
"He will be a big asset for this team and this squad if he can play to his level.
"Andy worked so hard and put a real shift in. He always does that and that's what you've got to understand with him.
"Not only is his form good at the moment, he is putting in a hell of a lot of hard work for the team."