Henderson has struggled to hold down a regular starting spot on Merseyside since signing from Sunderland in 2011, with the youngster almost joining Fulham in a part-exchange deal last summer.
The 23-year-old believes that his decision to stay and fight for first-team football has been vindicated in recent months, while describing Rodgers as a "brilliant" coach who has helped take his game to the next level.
He told The Telegraph: "I feel I belong here now. I got down when I wasn't playing very well. I'm probably my biggest critic.
"There was an opportunity that got brought to me [at Fulham] but I wanted to fight for my place. The manager was happy with that. Even when I wasn't playing, he was still helping me, which meant a lot.
"A lot of managers will forget about you. I always felt he believed if I could do the things he was saying, he would give me the opportunity and he did. I kept working hard and repaid the faith he had shown in me. The manager has been brilliant since he came in."
Henderson has featured in all seven of Liverpool's Premier League games so far this season, helping the Reds make a strong start to sit second in the table.