The Sky Blues let their fate slip out of their hands on Wednesday when Mario Mandzukic struck in the 18th minute, just after Fernandinho had missed a golden opportunity for the visitors.
The result meant Juventus leapfrogged City to top spot in group D and need only a draw from their final game against Spanish side Sevilla on Dec. 8 to go through as group winners.
City were guilty of having spurned a number of good chances in Wednesday's game and Toure also says the visitors could have clinched at least a point had they been more ruthless in front of goal.
"We had quite a lot of injuries from important players but we have to live with that," Toure told reporters after the game.
"We have a fantastic squad and I think we were unlucky to be honest. We have to forget this game and try to bounce back in the league."
"It's part of football -- to win, you have to score goals -- but we missed chances and these things can happen.
"We are quite disappointed. It was a 50-50 game and we had a lot more chances than them but we were not clinical.
"We had chances to score but at the end of the day, it was 1-0 for them and we have to bounce back in the next game."
The Sky Blues have now failed to win three consecutive games for the first time this season.
Manuel Pellegrini's side were without six first-team players for the trip to Italy, with Wilfried Bony, Pablo Zabaleta, Eliaquim Mangala, Vincent Kompany, Samir Nasri and David Silva sidelined through injury.
To add to their injury woes, goalkeeper Joe Hart was forced off the field on the 81st minute with a reported hamstring problem.
City will turn their attention to Saturday's Premier League game against Southampton as they look to get their title challenge back on track following back-to-back defeats.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
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