The England international is on-loan at Upton Park from Liverpool and despite a promising start and continued decent displays the 23-year-old is yet to hit the back of the net. Allardyce feels the club's supporters have noticed the work ethic of the former Newcastle forward and believes that will give him more time to find his shooting boots.
"The fans at West Ham love committed players and they love players who give their all and I think Andy wears his heart on his sleeve," he said.
"I think a part of Andy's frustration has been the amount of times he seems to be fouled these days but doesn't seem to get the free-kicks against him that he deserves.
"He has to understand that's probably always going to be the case but for him it's not to get frustrated by that it's about making runs in the right positions and just keep showing that commitment and eventually it will pay off for him and for us."
Former Blackburn boss manager Allardyce feels Carroll will be thinking about his lack of goals and admitted scoring early at a new club can prove vital for a striker.
"I don't think it helps you I think you like to come and start and get off the mark as quickly as you possibly can," he said.
"What I do think is that he's not just a goal scorer. That's 90% of his game. I think he's an all-round frontman in terms of his hold-up play and his movement as well as his ability to score goals."
Allardyce has also refuted claims that a lack of goals would start to affect Carroll's attitude. He said:
"No, I don't think so, I think he's a little frustrated by it but that's the issue. I think we're getting in terms of reading the situation, the more and more he plays with the players we've got, the more and more he can start to read how the situation develops and hopefully get on the end of it."