The England midfielder has taken the brunt of the criticism for his side's indifferent performances this season, collecting just 16 points from 14 Premier League matches.
Gerrard has scored only once in the league this term, but Rodgers insists he is still a great leader out on the pitch.
"He's carried this club for nearly 13 years, and it's about time there was more than Steven picking up the baton of responsibility for Liverpool," Rodgers said.
"He's been brilliant since I arrived here. His inspiration and leadership within the team has been phenomenal.
"He might not have got the goals that he wanted this season, but you saw him at Tottenham - his range of passing, commitment and drive into the box was superb.
"He has been judged on his goals because he's been a goalscoring midfielder over the years, but he's still offering this group so much on and off the field.
"There are others that we want to step up to the plate and get the goals. Across the board we want to improve and find the solutions."
Rodgers also confirmed that Lucas Leiva and Joe Cole could return to the squad for this weekend's clash with Southampton at Anfield.