City dropped to 22nd place in the 36-team standings, with only the top 24 advancing.
Progression to the next round of the new-look format looked a certainty before the season for the team crowned European champions in 2023 and having won the last four Premier League titles.
But not anymore as City manager Pep Guardiola battles injuries and an apparent loss of belief among his players.
City have won just one of their 10 matches in all competitions, with goals by Dušan Vlahović and Weston McKennie inflicting the latest defeat and igniting Juventus's qualification hopes.
City midfielder Ilkay Gundogan described the team's problem as a "mental issue."
Opponents "are able to break our rhythm with the smallest of things," Gundogan said. "They don't even need to do much and it has such a big effect on us right now."
Barcelona jumped into second place in the league standings, behind Liverpool, and are guaranteed to advance after a 3-2 win at Borussia Dortmund. Raphinha and Ferran Torres, with two goals, scored for Barca.
Arsenal beat Monaco 3-0 mainly thanks to two goals by Bukayo Saka to move into third place and be the highest of six teams on 13 points.
The top eight qualify directly for the last 16 and the teams placed No.9-24 go into a two-legged playoff.
City have two games to save their faltering Champions League campaign and the first is against Paris Saint-Germain, another giant in trouble in 25th place - one spot out of the qualifying positions.
Vlahović put Juventus ahead in the 53rd when he powered a header straight at City goalkeeper Ederson, who could only parry the ball over his own line. Two American substitutes sealed the win for Juve, with McKennie volleying home from Timothy Weah's cross, who moved to 14th.
Ferran Torres came off the bench to inspire Barcelona to a fifth win in six games and push Dortmund, last season's runner-up, out of the top eight.
Torres came on in the 71st to replace Robert Lewandowski, who had a quiet game against his former club. Just four minutes later, Torres scored a goal on the rebound from Dani Olmo's shot.
Serhou Guirassy's second goal of the game levelled the score at 2-2 but Torres scored again in the 85th off Lamine Yamal's pass on the counter.
Raphinha gave Barcelona the lead before Guirassy equalised from the penalty spot. Raphinha and Guirassy are tied for second place in the scoring chart on six goals, behind Lewandowski's competition-high seven.
Arsenal secured a third straight home win without conceding in the league stage, with Saka scoring in the 34th and 78th minutes and sending in a shot that was turned into the net by substitute Kai Havertz in the 88th.
Arsenal are ahead of Bayer Leverkusen, Aston Villa, Inter Milan, Brest and Lille on goal difference. Lille won 3-2 at home to Sturm Graz on Wednesday.
With a brilliant curling finish to open the scoring, Argentina striker Julian Alavrez helped Atletico Madrid beat Slovan Bratislava 3-1 and provide a timely reminder of what City is missing after selling him for more than $100 million in August.
Alvarez has 12 goals for the season, four coming in the Champions League.
Antoine Griezmann scored Atletico's other two goals at Metropolitano stadium as the Spanish team climbed to 11th place after a 10th straight win in all competitions.
Tammy Abraham scored an 87th-minute winner as AC Milan beat Red Star Belgrade 2-1 to move one point off the top eight. Milan lost Alvaro Morata and Ruben Loftus-Cheek to muscle injuries in the first half.
Benfica's five-match winning streak ended with a 0-0 home draw against Bologna, and Feyenoord had a 4-2 win over Sparta Prague.
