The former Leicester City boss saw his side lose 2-1 to the Serie club on Wednesday night.
Kyogo Furuhashi had given the hosts the lead, before Matias Vecino equalised, when the drama unfolded.
Rodgers cut a frustrated figure as Lazio snatched it late on at Celtic Park, with former Barcelona and Chelsea forward Pedro heading in Matteo Guendouzi's cross on 95 minutes.
The loss leaves Celtic bottom of Group E following back-to-back defeats, and Rodgers with the accolade of being the worst manager to have taken charge of 20 games in the Champions League.
Rodgers has won just two of his games in the competition, drawing five and losing the other 13.
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So out of the 87 managers to have taken charge of 20 games in the competition, none have won fewer than the 50-year-old.
Rodgers' last Champions League victory came back in 2017, when Celtic defeated Anderlecht 3-0 in Belgium.
His other was when in charge of Liverpool, a 2-1 win over Bulgarian side Ludogorets Razgrad in September 2014 at Anfield, when Steven Gerrard netted a last-gasp penalty.
Rodgers told TNT Sports, post-match: "Disappointed in terms of the result of course, but really for the players because they gave so much.
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"We scored a fantastic goal and we're disappointed with the one we conceded.
"Apart from one chance early on in the second half, we looked like we could go on and take it.
"Disappointed with the winning goal, you just have to secure the game at that point, that's just game management. Just that one moment of quality sees us lose the game.
"I can't fault the players for their effort shown in the game. I can't be critical of this group of players after what they gave. We should have had more from that game."