The Reds are currently 11th in the Premier League table having lost three of their first five games.
Merseyside rivals Everton, who themselves have made a slow start to the campaign, travel to Anfield this weekend for a crunch showdown, with Rodgers quick to praise his opposite number Roberto Martinez.
"We have looked a little bit broken," the former Swansea City boss told reporters. "We know we need to be better, and to improve our performance level. That's the key for us.
"[Everton] haven't had results they wanted, but they have quality. It'll be a tough game for us. Everton are a good side. They had a stable base and introduced a few more to that in the summer. Roberto has done an excellent job."
Liverpool follow up Saturday's game with a trip to face Basel in the Champions League.