The result leaves Celtic a near impossible task of overturning the deficit in Turin on March 6.
And it deals a fatal blow to their hopes of becoming the first Scottish club to reach the last eight of the competition.
Celtic manager Neil Lennon said after the match that his side would need a "miracle".
More than 60,000 fans turned Celtic Park into a cauldron of noise as the teams took the field.
But the die was cast within three minutes, when Juventus took advantage of slack Celtic defending to open the scoring.
Spirited play kept Celtic hopes of an equaliser high, but two more Juve goals in the final 20 minutes of play dashed any dreams of victory. Music legend Rod Stewart was in his usual seat, looking pensive, as the match unfolded and comedian Billy Connolly was also spotted in the crowd.
Fans who had been on the edge of their seats throughout the match were reduced to tears by the final whistle.
Lennon said afterwards: "The scoreline flatters Juventus. We need a miracle now. That's the harsh reality of Champions League football."
Socialist politician Tommy Sheridan tweeted: "Great Celtic performance for 1st 45 minutes but Juve class began to tell as the game progressed. No shame in losing to them. Heads up. Ref??"
TV pundit Pat Nevin praised Celtic's performance.He said: "Celtic for the vast majority of this game can walk away with their heads held high. They haven't been disgraced and played well for large parts of the game."
Former Liverpool defender and Big Brother contestant Neil Ruddock tweeted: "Felt the Hoops deserved more: Can't believe that's finished 3-0. Hoops must have had 70 per cent of the play!! Didn't like the referee."
Comedian John Bishop said: "Gutted for Celtic. Got to stop wrestling in the area! They deserve more than this."
Marseille midfielder Joey Barton said: "Curtains! 3-0. Did feel with the pace they played at from the start, it was not maintainable for the duration of a game. Marking from the corners for Juve, has been borderline GBH at times. I went to jail for much less."