Victor Osimhen's second-half double earned the Italians a 2-2 draw to deny the Foxes victory in their opening Group C game.
The striker levelled with three minutes left having pulled a goal back after Ayoze Perez and Harvey Barnes gave Leicester the advantage.
Wilfred Ndidi was also sent off in injury time for a second yellow card to add to the Foxes' woes.
Rodgers said: "It was a really good measure for us. Napoli are arguably the favourites for the competition but we were very competitive.
"We are disappointed to lose the goals but there is still a lot for us to be happy about and lots for us to analyse where we can do better.
"It was a really exciting game for the neutral, I was really pleased with the team in terms of the mentality, the goals and the resilience for a lot of the game.
"I didn't think the referee was very good all night and Wilf was unfortunate, he picked up the booking early on and was fighting to get across to stop the attacker getting away. It was a little bit harsh."
Tensions also flared between supporters at the final whistle with missiles thrown between the home and away fans. Police and stewards needed to stop scuffles breaking out as fans attempted to break through to each other.
With just the group winners going through automatically it could be two crucial points dropped for Leicester and increases the pressure for the trip to Legia Warsaw - who won at Spartak Moscow - in two weeks.
Perez gave the Foxes the lead after nine minutes when he volleyed in Barnes' deep cross but the hosts lived dangerously as Napoli created and wasted chances.
Osimhen fired over, Piotr Zielinski was denied by Kasper Schmeichel and Timothy Castagne, Lorenzo Insigne shot wide with Schmeichel also saving Hirving Lozano's header.
The Foxes lost Jonny Evans to his long-standing foot problem at half time and Patson Daka had a goal disallowed by a tight VAR offside call
But Barnes doubled their lead when he fired into the corner after being picked out by Kelechi Iheanacho.
Yet, Osimhen sparked Napoli's comeback after 69 minutes when he lifted over Schmeichel following a slick move and completed it when he headed in from eight yards with three minutes left.
Ndidi was then dismissed in stoppage time for hauling back Adam Ounas for a second yellow card.
Napoli boss Luciano Spalletti said of his team: "They played a great match, they challenged the opposition with a strong mentality and there were some very important steps forward made.
"What probably made the difference after 2-0 was the continuous strength, conviction and self-belief to be able to get over being 2-0 down. The substitutes made a really important contribution.
"You often don't realise how important the impact players are. They truly gave that strength and freshness.
"You have to look deep and far to find any fault. They did what they had to do when others teams might have felt disheartened or weak."