Neil Lennon's side fought bravely after getting off to the worst possible start in their Champions League last 16 clash when Alessandro Matri netted in the third minute.
But two further strikes from Claudio Marchisio and Mirko Vucinic put the Italian champions out of sight – and left Celtic acknowledging that their European dream is over.
"Yeah, we need a miracle," said Lustig. "It is going to be very difficult for us. We knew before the game that it would be tough because Juventus are one of the best teams in Europe. I think we played well against them and we tried to play football.
"It would be very hard now for us to come back from that. But we want to keep our pride.
"We need to try and compete next month in the second leg in Turin. We want to show that we are a decent football team."
Ultimately, the last 16 of the Champions League has been a bridge too far for Celtic side this season.
They showed spirit and guile at times against Juventus, particularly in the opening half, but too many individual mistakes proved to be enormously costly.
Efe Ambrose was the worst culprit and was responsible for two goals. Lennon will doubtless have cause to rue his decision to throw in the Nigerian, who returned to the club on a high following his Africa Cup of Nations victory with his country on Sunday.
Ambrose has gone from the high of that success to the hollow unease that engulfed him as he lay slumped on the Parkhead turf after gifting possession in the build-up to Juve's third.
Lustig, though, was reluctant to point the finger at his team-mate.
"Of course I felt for Efe after the game," he said. "No one knows more than him that he made a few mistakes in the game. It is a team game and I am sure he will get over it.
"When you are playing at this level mistakes are punished."
Despite the deflation at the result, Lustig believes that Celtic have still benefited from being at this stage of the competition.
There is an argument to say the Parkhead side may well, in hindsight, feel that a Europa League place may have enabled them to continue a European journey this season.
"No, we wanted to qualify from the group and we were pleased when we achieved that," he said. "It was a good experience for us to play against a team like Juventus.
"We lost our way a little bit when we lost the second goal but I think we have showed this season that we can compete in the Champions League.
"We created chances against one of the best teams in Europe. We tried to play with confidence and on another night, if one of those shots had gone in, then you just never know what might have happened."