The Merseyside outfit have parted ways with the Uruguayan, who scored 31 Premier League goals last season, after agreeing a reported £75m fee with Barcelona.
Despite losing their prolific forward, Sturridge believes that there is now an opportunity for new faces to take responsibility for goals.
"People have to step up," Sturridge told Jamaica's Nationwide Radio. "When stars leave, a new star can be born, as they say.
"There are a lot of players that can take that mantle, but it is a team game, regardless of whether there are star players within that team. It's not about one person, it's about the team."