The Hammers made the forward their club-record signing when they paid Liverpool around £15m for his services in the summer of 2013.
However, the England international has struggled with injury and spent most of his first term out with a heel problem, while he is also yet to play this campaign after suffering ankle ligament damage.
"I don't feel I've let them down because, obviously, it's an injury that I couldn't have helped," Carroll told reporters. "I've done it in training and in a game. It's an injury I don't want and obviously no one at the club wants.
"I do want to be back out there, repaying the faith they put in me. I don't really care what people say. I know I've had problems. I'm not hiding away from that.
"Hopefully, this is the last one, and I get it out of the way. I just want to get back playing football."
Carroll recently admitted that he is around "two weeks" away from returning to training.