Like his team, Gerrard, 34, has endured a difficult start to the campaign with Liverpool losing three of their opening five Premier League games.
But Rodgers said the team as a whole needed to take responsibility, including for Saturday's 3-1 loss at West Ham.
"I have no concerns," Rodgers said about Gerrard.
"He's a brilliant player for us, really talented. It was a team performance that was not up to scratch against West Ham.
"We have conceded eight goals and the majority of those could have been avoided. But for us as a team, we need to be better.
"We're still looking to find our performance level, which apart from Tottenham, we've not been at."
Rodgers said he had been pleased with the way the club were dealing with Gerrard, who played 270 minutes in a week culminating with the West Ham loss.
"We have managed his recovery really well in the last two seasons, even when Steven was playing international football," he said.
"If you look at his numbers and games, they have been as good as ever.
"He is at the age where we need to treat him individually. We want him to be involved in the big games because of his experience and we will always taper that recovery to allow him to be the best he can be."
