The Gunners made seven changes at the King Power Stadium as a Christian Fuchs own goal and late Eddie Nketiah tap-in sealed a 2-0 victory for the visitors.
Despite those alterations there was still no room in the matchday squad for either Ozil or Matteo Guendouzi, who have yet to kick a ball this season.
“There were moments of quality in it and even though there were lots of players playing their first minutes of the season the cohesion in the team was very good.
“I’m obviously disappointed with the goals, that was the only criticism – it was two scruffy goals that we lost to.”
Wilfred Ndidi was not involved for Leicester and Rodgers revealed after the match that the Nigeria international may be sidelined for up to 12 weeks with an abductor injury suffered against Burnley.
“We are just waiting to hear more on that, but he could be anything between six and 12 weeks,” he said.
“It is an abductor injury – it may have come off the bone which could be a nasty injury, so we will wait to see if needs an operation – it does then it will be 12 weeks.”