Rodgers spoke after Sunday's scrappy 2-1 Premier League win over Southampton about his desire to bring a genuine goalscorer to the club in the wake of Suarez's departure to Barcelona.
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"More goals from everyone - that's the objective," Rodgers told the club's official website. "Everyone will want to improve. Raheem [Sterling] had 10 goals last year.
"It was a great pass by Jordan [Henderson, who set up Sterling's opener on Sunday]. He picked him out really well with a wonderful ball and he gets himself in the box with a wonderful finish.
"It was a really good finish and that started to open up the game a bit, with a bit more space to work in. But they were dangerous opponents."
Liverpool scored 101 goals in the Premier League last term as they finished second, just two points behind Manchester City.
Only three sides have scored 100 goals or more in a Premier League season in the last 10 years, with Chelsea, in 2009-10, and City – last term – achieving the feat.