Neil Lennon's side were on the end of a clinical and ruthless display from the Italian champions, who withstood some sustained pressure, especially in the first half, to all but seal their place in the last eight.
But Celtic right-back Mikael Lustig refused to give up all hope of upsetting the odds in Turin on March 6.
The Swede told uefa.com: "It's almost mission impossible but miracles have happened in football before.
"You never know - a penalty, a red card then maybe we're back in the game, but it's really tough now."
Celtic midfielder Kris Commons also held on to some optimism despite his bitter disappointment at the heavy defeat.
Commons said: "We won't be going over there thinking the tie is over. We've got a good set of players and our coach won't let us believe this tie is over.
"If we have a really good night and they play poorly, you get a couple of early goals you just never know, so we'll be going over trying to stamp our authority on the game and get an early goal - that would be ideal for us."
Commons came close on a number of occasions during a first half largely dominated by Celtic, even before Alessandro Matri capitalised on a misjudgement by Efe Ambrose to net in the third minute.
Victor Wanyama and Ambrose both missed excellent headed chances and Celtic paid the price in the final 15 minutes.
Claudio Marchisio grabbed a second following a slick counter-attack and Mirko Vucinic finished after another mistake by Ambrose, who had only returned to Glasgow on the morning of the game after playing for Nigerian in their African nations Cup win on Sunday night.
And Celtic can rightly take some encouragement from their general play as they plot an unlikely comeback.
Commons said: "We had some good build-up play and possession which got us in good areas.
"The keeper made some good saves but you get paid for what happens in both boxes and we couldn't quite get a goal and conceded three sloppy goals which near enough ends our run in the competition.
"It's hard to put into words when those kind of mistakes are happening at this level.
"It's frustrating but it was one of those games where individual mistakes cost us the game.
"They're a good team but in the first half I think when we put them under pressure they gave the ball away, but in front of goal they were clinical."
Lustig added: "Three-nil is not a good result but I think we played really good in the first half.
"Even at 1-0 we were more than a match for them and had a lot of chances but we couldn't score.
"Juventus probably are one of the best teams in the world, so if you let them get chances like that they're going to score.
"I don't think Juventus are totally satisfied with their performance either, especially in the first half, but football is about scoring goals. They scored three and we didn't."
The visitors admitted their clinical edge won through.
Marchisio said: "It was a difficult match. Celtic caused us a lot of difficulties, particularly in the first half, but the team managed to keep up the pressure and bring home a very important result, because scoring three away goals counts for a lot.
"Taking our chances and scoring was important. We definitely created less than Celtic, but in the end we were more clinical and managed to secure this win."
Goalkeeper Gianluigi Buffon added: "We wanted to play the game as we normally do, attacking and pressing our opponents, but we had to face a team which caused us difficulties in the build-up of play, and it was a very intense atmosphere.
"That's why we tried to have trust in ourselves, defending a bit, being dangerous on the counter, and being clinical with our chances.
"The result says it was easy, but the match was very difficult to play.
"It was pretty hard, and as I said it was determined by certain situations which were basically all in our favour.
"That's why we achieved such a solid result here, but Celtic showed themselves to be a great team."