The Northern Irishman endured a tough induction as he replaced club icon Kenny Dalglish and having reached mid-October with just one Premier League victory he found everything from his suitability to his methods called into question.
But after a number of early-season setbacks the Reds boss thinks the club is beginning to show signs of recovery and will continue to grow in line with his long-term plan.
"If you believe in a manager and put him in place and give him time what has been proven in this country is that can lead to success," he said. "I think those early months were always going to be difficult; you are trying to instil and implement ideas initially without a great deal of success.
"Those early months could have been difficult but in terms of myself, players and staff we were very much focused on our job and there has been no change in ourselves, only improvement. All you can do is have an inherent belief in how you work and I believe this is the way the club wants us to work."
Rodgers added: "I have been grateful to the board here because in order for me to come here that (support) was something which was going to be important because if we were going to keep the club moving in the right direction it was going to need some stability."