Rodgers has sought to implement a faster, more fluid, expansive passing style at Anfield this term, bringing in the likes of Joe Allen, Daniel Sturridge and Philippe Coutinho to help realise his vision.
The Reds have earned plaudits for their performances under the Northern Irishman, but Gerrard is challenging his team-mates to turn their pretty play into tangible rewards.
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"I think we're starting to see the rewards but there's a long way to go obviously; we all know where we want to take this club.
"The fans here deserve to see trophies and Champions League football. That's what Liverpool is about."
After a controversial and patchy first year in England, Luis Suarez has re-found his scoring touch this term, notching 28 goals in 38 appearances, and Gerrard insists the Uruguayan is a great dressing room influence.
"As a person he’s a quiet guy, a family man; I am next to him in the dressing-room and every time I ask him what he’s doing he’ll say he’s going to be with his family," he continued.
"But when he goes on the training field or a football pitch he turns into a winner. When you are trying to win prizes against the top teams, Luis Suarez is someone you’d want in your side."
Gerrard also revealed his disappointment at team-mate Jamie Carragher's decision to retire at the end of the season, admitting he will miss the advice and presence of his friend within the team.
"I’ve tried just as hard as everyone else to try to keep him going for a bit longer, but we have to respect his decision," he continued.
"He’s had a fantastic career and he feels it’s the right time to go out, at the end of the season. Hopefully there are still some big performances left in him before he goes.
"Everyone knows what we’re going to miss [from] him on the playing side. Since I made my debut Jamie has been alongside me in the dressing room and been a close mate of mine.
"It’s going to be different and no one is going to miss Jamie more than me."