The Reds welcome the Swiss side to Anfield for a crucial fixture as they sit level on six points in Group A - second and third respectively - but Rodgers is confident his vision is beginning to bear fruit.
With Roberto Di Matteo shown the exit door at Chelsea on Wednesday, Rodgers believes the Liverpool board's understanding has helped him begin to turn results around.
He said: "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.
"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.
"As a manager, in order to fulfil what you want to over the longer term you have to take care of the short term - that was something I learned in my job at Reading.
"I was given a three-year contract and took the job in the great belief I was brought in to change the philosophy and ideas of the club and 20 games later I was out of a job. That was the harsh reality of managing a football club and from that I learned a lesson.
"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."
A shaky start to the season has given way to some more positive results of late despite a lack of options in attack, with Liverpool unbeaten in their last seven Premier League games.