Goals inside the first 30 minutes from Lawrence Shankland and Stephen Kingsley were enough to help Hearts claim their first win at Parkhead since 2007 and condemn a below-par Celtic outfit to their second successive league defeat following last weekend's 2-1 loss at Kilmarnock.
The atmosphere turned toxic at full time as Celtic fans called for the club's board to be sacked, while Rodgers' players were booed off down the tunnel after the Parkhead faithful watched their side's 52-game unbeaten league run on home soil come to an end.
Rodgers vented his frustration after the match, telling celticfc.com: "I felt that our desire in the game and our passion in the game was nowhere near it in terms of when we started, and we were too passive.
"If you look at the first goal, we got blocked off so easy, so we were very naïve and then we give away a poor second goal.
"It was a great free kick but if you look at the lead-up to that, the passive nature of our game - there was intensity there - and eventually they come through to our final third and get the free kick.
"I was disappointed with our authority and that mentality and desire to go and win the game. We got into some good areas for a lot of the afternoon but we never had any real decisive moments.
"Their keeper's made some good saves but the feeling was that we'd maybe go through another hour and maybe not score.
"But overall, I think the desire and that passion to play with that real intent was missing. It was better in the second half but still nowhere near a Celtic team."
Responding to the fans' criticism of the board, Rodgers added: "You do your talking on the pitch and today was on myself and the players. Today was nowhere near the level of a Celtic player and that is something that falls on me. So I need to find the answers for this group and to ensure we can gain that consistency in the team."
Celtic have missed the chance to extend their five-point lead at the top of the Premiership table, and the reigning champions could slip to second if Glaswegian rivals Rangers - who face Aberdeen in the Scottish League Cup final on Sunday - win their two games in hand.
"It's great when you're stood on the touchline and winning five or six-nil, but when you lose 2-0 against Hearts at home and you make a poor performance, this is where you get judged," Rodgers added.
"So we need to reflect on the game and get away and get ready for next week, and produce a much, much higher level and standard of performance than we did today."
Celtic will now turn their attention to next weekend's home encounter with Livingston, before ending the year with two more league games against Dundee and Rangers.