Manager Brendan Rodgers showed the £35 million striker the door at Anfield despite failing to bring in a replacement.
Carroll scored just 11 goals in 58 games for Liverpool, but earned a place in England's Euro 2012 squad with some impressive performances in the spring, which included a goalscoring cameo in the FA Cup final.
"I haven’t got a fair chance at Liverpool, and I was told that I should move on to a team where I’ll play regular football," Carroll told ESPN.
"I kept my head a lot, and I could have lost it at Liverpool but I got my chance when we went away to the Euros and I took it.
“I know what I’m capable of and if other people don’t believe it then that’s fine really; I’ll just get on with it.”
The England striker is expected to return from injury for the Hammers' game at home to Arsenal on Saturday afternoon.
