As things stand, Carroll remains a Liverpool player, but the 23-year-old disclosed how West Ham manager Sam Allardyce offered him the regular first team football that was not on the cards for him at Anfield.
"I haven’t really had a fair chance at Liverpool," Carroll told ESPN.
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"Obviously, I didn’t really get a chance there."
Despite holding the title of Liverpool’s record signing at £35 million, the former Newcastle icon was never able to hold down a regular starting spot on Merseyside, a situation that was exacerbated by the arrival of Brendan Rodgers in the summer.
"A new manager came in and I wasn’t part of his plans," Carroll claimed. "For me to play football, that was my chance to do that. That is why I am here at Upton Park.
"I think I could fit into every system. I believe in what I can do. Obviously [Rodgers] has his beliefs and he didn’t think that.
"But for me, obviously, it was better to move on instead of waiting for my chance - which he told me might not come."
Carroll also spoke of his happiness at scoring for Roy Hodgson’s England at Euro 2012, and of his determination to use his chance at Upton Park to prove himself as a striker of international pedigree.
He said: "The work I put in over the season, I deserved that goal. I kept my head a lot when I could have lost it at Liverpool. I got my chance at the Euros and I took it.
"Coming here, I have got a great chance to start games and score goals, which I haven’t really had many of last season.
"I don’t think I have got a point to prove, that is the wrong way to put it. I know what I can do and the ability I have got. I know what I am capable of.
"If other people don’t believe it, that is fine. I just get on with it. But at the end of the day, I know what I can do."