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The second-placed Foxes are now 10 points behind Premier League leaders Liverpool and face the Reds at home on Boxing Day after a trip to Manchester City next weekend.
Leicester paid a heavy price for a poor start as Teemu Pukki put the Canaries in front before a Tim Krul own goal brought Rodgers's men level before the break.
However, Leicester lacked their usual zip and Norwich's excellent defensive display frustrated the hosts to pick up a deserved point.
"Norwich started bright and deservedly went in front but second half we were much better," said Rodgers.
"It just looked like one of those games. It's a point and we need to look forwards now.
"The players have been brilliant. When you are on that winning run you believe you are going to win every game, but of course it does not work like that. We were not 100 percent on it. We need to set the reset button."
Second-bottom Norwich move to within three points from safety and Daniel Farke will be frustrated his side have not shown this level of defensive discipline on most of their road trips so far this season.
"It was our best performance of the season, at this moment and with this opponent," said Farke.
"In the first half we were the better side, even in terms of chances we were probably the better side in the second half and pretty close to winning the game."
Other than an early fumble from Krul, when he turned Youri Tielemans's drive onto the post, the visitors settled well and should have gone ahead when Sam Byram crossed for the unmarked Pukki, but the stretching striker could not turn the ball in.
Moments later, the Finnish international made amends by netting his ninth goal of the season on 26 minutes.
Norwich opened up the Foxes again when Emi Buendia slipped in Pukki to outpace Caglar Soyuncu and beat Kasper Schmeichel with a low finish.
But Farke's men undid a lot of their good work to allow Leicester level seven minutes before the break.
Jamie Vardy thought he had scored for the ninth straight game when he touched on James Maddison's corner at the near post.
However, as his header was flashing across goal, Krul's attempted save turned the ball into the net and the Dutch 'keeper was credited with the own goal.
Krul was almost beaten again two minutes into the second half when Vardy latched onto Maddison's pass, rounded Krul and rolled the ball onto the outside of the post from a tight angle.
Norwich offered little going forward after the break as they focused on keeping Leicester at bay.
Wilfred Ndidi nodded wide after 67 minutes but the hosts lacked inspiration and ideas, even if Krul was forced into a another smart low save by Vardy.
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