The 25-year-old scored the opening goal against Sunderland last night before Mohamed Diame netted what turned out to be the winner in a 2-1 victory at the Stadium of Light.
After the game, Allardyce told Sky Sports News: "If you want alternatives, Andy gives you one. He's unique in many ways. Not many can receive the ball and head a ball as good as he does, especially with quality balls in the box.
"Nobody was going to stop him for that goal. He has a lot more on the deck than people give him credit for. If he plays every week, scores goals, hopefully he'll go to Brazil."
Carroll was part of Hodgson's squad for the 2012 European Championships in Poland and Ukraine.