The 11-goal man has been ruled out for up to two months with an ankle problem and his usual partner, Suarez, cut a frustrated figure as a lone striker during the 3-1 defeat at Hull City on Sunday.
Summer signings Iago Aspas and Luis Alberto are both yet to make a real impact on the Premier League since their arrivals, but Rodgers thinks that they could now be ready to step up to the plate.
"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," he told the Liverpool Echo.
"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.
"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.
"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.
"It was too predictable. Certainly you wouldn't have said that about us in the last number of months.
"We are normally exciting and create lots of chances. We are on the front foot. We conceded a poor goal which put us on the back foot but we needed to be more dynamic. That is something we will look to put right."
Rodgers also defended duo Victor Moses and Raheem Sterling after the pair came under fire for their performances in the KC Stadium loss.
"Both players are very talented," he said.
"When we lose a game, we all get criticised but I thought both players worked hard in the game.
"Raheem is still only 18 years of age. He's been in and out this season but is still a fantastic talent.
"Victor has great ability. It's been a bit difficult for him as he hasn't had a run in the team but he's still a very important player for us."
Another concern for Rodgers has been Liverpool's pairing in the centre of the defence since Jamie Carragher's retirement last season.
Despite Kolo Toure, Mamado Sakho and Tiago Ilori all being brought in over the summer to compete with Daniel Agger and Martin Skrtel, the Liverpool boss admits he is still trying to find the right partnership.
"It's probably the first job I have been in where there have been lots of areas I have been happy and settled in but this is an important area," he said.
"It's something I need to look at in order to get that consistency. There has been lots of change - and some of that has been down to me - knowing every game is an absolute cup final for us.
"If I feel I have needed to change it going into a game to get a result, then I will do.
"But of course I also need to look at it from the coaching perspective as well, that a little run in the team might breed the consistency even though we have had to change a number of positions."