The 25-year old centre-forward is yet to play this season after suffering an ankle injury in pre-season which places him in a precarious position due to the form of summer signings Diafra Sakho, Mauro Zarate and Enner Valencia.
Former Liverpool striker Carroll, who cost the Hammers £15million last summer, is aware his time may be running at Upton Park but suggests he has what it takes to fight for a starting position in Allardyce's improved XI who currently sit seventh on the Premier League table.
"I don't mind a battle, and every team needs competition for places," he told the London Evening Standard.
"That is one of the things we have here. Everyone is fighting for their place.
"It has been mixed emotions for me watching the team this season. I am desperate to be out there on the pitch but I remember the Liverpool game when I was jumping up and down watching from the box. I think I did enough work for that day on my ankle!
"I know I've had problems with injuries and I'm not hiding away from that.
"Hopefully this is the last one and I can get it out of the way. The club have put a lot of faith in me, paying so much money, but I don't feel like I've let them down. It's an injury that I couldn't help."
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