The striker has not played since injuring his thigh while on international duty with England in September before damaging his calf during training in October.
Sturridge was expected to make his return for Liverpool following the most recent international break before pulling up in training for a second time on Tuesday and is now out for up to a further six weeks.
"Daniel has just been extremely unfortunate. He's a player who doesn't want to be out for this period of time with the quality he has," he told reporters.
"I spoke to Daniel at length and he's as down as I've seen anyone. We need to go away & find answers so he can perform consistently.
"I have great trust in the players. I would be more concerned if they were moping around or didn't care."
Liverpool travel to Crystal Palace on Saturday for the first time since losing a 3-0 lead to draw last season and severely dent their title hopes - but Rodgers feels the late collapse was not key to their failed bid.
"That wasn't the game that cost us. Maybe the excitement to claw back the goal difference overtook us," he added.
"The damage was always done in the Chelsea game. That was the one that changed it for us. But on reflection I was extremely proud."
"It will be equally as tough v Palace.Warnock is a wonderful manager with big experience. Look to start off exciting run with a win."