Carroll has endured an injury-ravaged time at Upton Park since becoming West Ham's £15.5 million club-record signing in 2013 - the latest being an ankle problem.
The 25-year-old England international striker underwent surgery in the United States in July, sidelining him for the start of the 2014-15 Premier League season.
Carroll, however, is on the road to recovery, back "running for the last 10 days" with a December return on the cards.
And the former Newcastle and Liverpool has backed himself to rediscover his best form with West Ham, having only managed 15 Premier League appearances following his permanent switch last season.
"I don't feel I've let them down because, obviously, it's an injury that I couldn't have helped," said Carroll.
"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."
