The visitors profited after Carroll combined intelligently with Ashley Young for the latter to score the only goal of the game in Oslo.
The striker had missed a close-range header in the opening minutes of the game, but he put that behind him in a determined display on Saturday evening.
And Hodgson told Liverpool's official website after the game: “I thought Carroll was good. He performed very well. He was not only good for us when we had the ball but also very important for us defensively.”
The £35 million forward’s club colleague and England team-mate, Gerrard, was also quick to laud him, adding: “I think Ashley Young and Andy Carroll looked good together.
“Andy put a really good shift in for the team. We got a win - that's the important thing. We got a win for the team."