Gerrard scored the winner from the penalty spot yesterday as Liverpool recorded a 2-1 success over struggling Aston Villa in the Premier League.
Rodgers has revealed that Gerrard and Jamie Carragher have been a constant source of support since he arrived at Merseyside last summer.
He told the Daily Mail: "Steven told me [from day one] that he and Carra would be 150% behind everything that I do.
"From that day they have actually been 200% behind me. They are phenomenal men, proper Liverpool people who want the club to do well and respect the role of the manager. He (Gerrard) is a top, top player, whose hunger and desire for Liverpool to succeed are remarkable.
"I can't speak highly enough of him. As a guy coming from the outside who has watched him playing, to come and work with him as a man is a huge pleasure and privilege. He will continue to be influential for the next number of years."
Liverpool sit seventh in the Premier League following their victory at Villa Park and are now three points behind city rivals Everton.