Leicester took the lead in the 9th minute through Ayoze Perez's strike before Harvey Barnes increased the lead in the 64th minute with a superb finish.
But Napoli's Victor Osimhen secured a point for the Italians with two great finishes in the game.
Leicester were on the verge of leading Group C following a draw fixture between Spartak Moscow and Legia Warsaw but squandered the opportunity in the dying stage of the game.
And not being satisfied with the result, Rodgers wants his squad to pick a lesson from the game as the season continues.
"The crime isn't giving away the two goals, the crime is if you don't learn from it. I'm sure that is something this young team will do," said Rodgers.
"I'm disappointed with the end result but there were some exciting and good moments," added Rodgers.
"The two goals are outstanding and the one that was disallowed was tight.
"Maybe we tired a bit. There are things for us to improve on - like keeping the ball better for longer periods. If we did that, we wouldn't tire so quickly.
"The effort and mentality was good. It is a shame we couldn't close it out."
Leicester, who have won two games and lost two in the Premier League will travel to Brighton on Sunday as they hope to return to winning ways.
