The Foxes are yet to hit top gear this season ahead of Sunday’s trip to Brighton.
They lost a 2-0 lead against Napoli to draw 2-2 in the Europa League on Thursday to continue a mixed start to the campaign.
Leicester have lost to West Ham and Manchester City in the Premier League and have beaten Wolves and Norwich, but Rodgers expects more progress as they find their feet this term.
He said: “There’s no doubt we need to improve and that’s something I’m very confident we’ll do throughout the remainder of the season.
“It’s still so early. I think everyone will assess it after 10 games and see where it’s at. It’s still so early, you’re still trying to get your rhythm and get your players up to a level of fitness as well.
“The competition is always very challenging and the top teams who were strong last year have invested in big players so they expect to be up there.
“The likes of ourselves will look to fight and compete against that.
“The players have been magnificent in terms of their attitude and mentality. They are always in the game, fighting, running and working – doing all the unglamorous stuff, as I say to them, which they do as everyone saw against Napoli.
“But we have to be better with the ball, especially when you play a team like Napoli, then for sure, you need to have a higher technical level to compete.”
Ayoze Perez, who scored the opener on Thursday night, serves the final game of his suspension after getting sent off at West Ham last month.
Jonny Evans is also expected to miss out after coming off at half-time against Napoli as he continues to struggle with a foot problem.
It is the same issue the defender battled with last season which also forced him off early in the FA Cup final victory over Chelsea.
Rodgers added: “We’ll just need to wait and see. He’ll probably struggle for the weekend. He’s felt his foot again so we’ll see, medically, how that looks in the next couple of days.”
Brighton have won three of their opening four games this season and Rodgers remains a fan of what boss Graham Potter is doing at the Amex.
He said: “I have a big admiration for his work. When Chris (Hughton) was there, he did a fantastic job in a different way. There is no right or wrong way to do it.
“When you come in, one of the biggest things you have to do as a manager is to convince players of how you want them to play and he’s been able to do that.”