The 35 million pound striker admitted he could have lost his head in frustration over his Anfield situation last season.
The England forward moved out on loan to West Ham United in August, and has so far helped the Londoners to seventh place in their first season back in the Premier League.
But the 23-year-old insists he would adapted his game to play in Rodgers' system if he'd stayed on Merseyside instead.
"I haven't really had a fair chance at Liverpool. I was really told that I should move on to keep playing regular football, and obviously then Sam wanted me here and told me I would be playing regular games," the Daily Mail quoted Carroll, as saying.
"So, for me it was a no-brainer coming here and to play. Obviously, I didn't really get a chance there. A new manager came in and I wasn't part of his plans. For me to play football, that was my chance to do that. That is why I am here at Upton Park," he added.
"I think I could fit into every system. I believe in what I can do. Obviously he [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," he said.
Carroll added: "Coming here, I have got a great chance to start games and score goals, which I haven't really had many of last season." (ANI )