Rodgers succeeded Dalglish last week with some Liverpool supporters doubting whether the Irishman has the experience of the stature to replace Anfield's most revered player and coach.
"As the chairman said, he is the heart and soul of this club. His love for this club is unrivalled. He is the best player in the history of this club.
"This is a prestigious club and this is a guy who has a wonderful history here and will continue to have a great future in terms of Liverpool. I can't worry about that. I can't say anymore about a man I respect.
"The only way you can overcome that is by winning. I am not here to win any race or competition. But what I know is history judges you as a manager and hopefully in time people will look back at what I have achieved here and I can walk beside these people.
"But there is no way I can try and overtake someone like Kenny Dalglish. All I can do is be myself."