Rodgers' side have just two wins in five Premier League games and needed a marathon penalty shoot-out to overcome Middlesbrough in the League Cup on Tuesday.
The Northern Irishman has admitted Liverpool are well below their best, but feels that can change starting with Saturday's clash against Everton.
"It is a big game for us and we need to get our league season up and running," Rodgers told Sky Sports after his side's win over Middlesbrough.
"There is no better game than a derby."
Rickie Lambert and Adam Lallana got much-needed game time in the League Cup, with the former captaining Liverpool.
Rodgers praised Lambert and said the striker knew his role this season would be mostly off the bench.
"Rickie has done really well coming off the bench. He was aware that was going to be a permanent role," Rodgers said.
"It was a great honour for him to captain the team being a Liverpool lad."
Rodgers said Lallana was still working his way to fitness after missing a bulk of pre-season with a knee injury.
"Adam is still probably in his pre-season phase because he hasn't played over the course of pre-season due to injury," he said.
"So for him to get the game time was really good."
