With the Reds looking short on options up front, the Northern Irishman wants his Spanish summer signings to step up after taking some time to adapt to life in the Premier League.
Both Spanish forwards - who joined the English outfit in the summer - have failed to score in their respective six Premier League appearances to date.
However, with Sturridge sidelined for up to two months with an ankle injury, Rodgers needs players to step up and support Uruguay star Luis Suarez.
"We can't just rely on Luis for goals," he told Liverpool's official website. "The likes of Aspas and Alberto have been at the club for a few months now and have seen the difficulties of playing in the Premier League, how hard it is and the physical demands. I can see them improving and working hard to fit into it. They will get improve and get better in time. There was always going to be a period of adjustment."
Even if the duo performs, Rodgers said, everyone at the club should raise their game in Sturridge's absence.
"With Daniel out, other players who have been working hard will get an opportunity. We now have to find a different way to win games. We can't just rely on one player for goals. It's the responsibility of everyone," he said. "It has to be for everyone to create and score goals. If some aren't available, we need to do more as a team - that was the message after the defeat to Hull."
In a boost for Liverpool, Philippe Coutinho is likely to return to the starting lineup against Norwich City on Wednesday after overcoming an ankle strain.