The England international moved to Upton Park on loan in August but believes that the arrival of Rodgers at Anfield was key factor in the move.
Carroll told ESPN: "I have't got a fair chance at Liverpool. I was told I should move on to a team where I'll play regular football.
"I knew Sam wanted me here and told me I'd be playing games so for me it was a no-brainer coming here.
"I think that happens in lots of clubs, a new manager comes in and doesn't give some players a chance straight away."
Carroll lined up for the Hammers in Saturday evening's clash with Arsenal and you can follow coverage of the fixture here.