The Reds have lost their prolific striker Luis Suarez, who scored 31 Premier League goals last term, after the Uruguayan opted to join Barcelona for a reported £75m fee this summer.
"More goals from everyone, that's the objective," Rodgers told the club's official website. "Everyone will want to improve."
The Reds have made eight signings so far this summer following the acquisitions of Rickie Lambert, Adam Lallana, Emre Can, Lazar Markovic, Dejan Lovren, Javier Manquillo, Divock Origi and Alberto Moreno.
Despite their heavy spending, Rodgers recently reiterated that the club are hunting for a new striker following the departure of Suarez.