Ambrose was part of the Nigeria team which triumphed in South Africa but he was at fault for Juve's third minute opener by Alessandro Matri, missed a key chance at 1-0 in the second period and faded badly as the Italians raced away.
Claudio Marchisio and Mirko Vucinic netted after 77 and 83 minutes with Ambrose floundering to all but put the twice European champions into the quarter-finals with Celtic facing a monumental task in Turin in the second leg on March 6.
"I think the scoreline flatters Juventus. I thought for the best part of the game, for the first 70 minutes until the second goal, we were by far the better side but you can't give away sloppy goals like that," Celtic manager Neil Lennon told ITV.
"[Ambrose] was poor for the first goal. We've switched off defensively for the second goal and the third goal was poor.
"We need a miracle. That's the harsh reality of Champions League football."
The Scottish champions did beat mighty Barcelona at home in the group stage but even those heroics will pale by comparison if they somehow knock out the Italian title holders and league leaders.
A rugged Juve had to fight in the first half against a fast and furious British pace they are not used to in the more leisurely Serie A and jubilant goalscorer Marchisio was already looking past the second leg.
"Tonight we have given out an important signal. The result was crucial because it allows us to concentrate on the domestic league," he told Mediaset television.
CELTIC ONSLAUGHT
Juve goalkeeper Gianluigi Buffon had tried to play down the impact of Celtic's famously noisy fans ahead of the match but even the coolest of Italians would have struggled not to have been affected by the almost 60,000 screaming home supporters.
Almost all of the Celtic fans stood with scarves aloft and sang a stirring rendition of "You'll Never Walk Alone" before kick-off but soon they were cursing their luck after Ambrose's feelgood factor from Nigeria's title win quickly evaporated.
The centre-back got caught out by a ball played over the top of the defence and Matri easily outmuscled him before prodding it between goalkeeper Fraser Forster's legs.
Wilson ran back to hook it away and although the ball had already just crossed the line, Marchisio fired home the clearance just in case.
That was the only real chance Juve had in the first half as they were then forced to withstand a Celtic onslaught.
Commons was just wide with an overhead kick in the pick of their chances while midfielder Victor Wanyama also twice went close as Celtic looked to storm back and win like they did 4-3 in their last home meeting with Juve in 2001.
Andrea Pirlo clashed repeatedly with Scott Brown in the midfield but Lichtsteiner's continuous battle with Gary Hooper at corners as the Celtic striker tried to block Buffon could easily have warranted a spot-kick or red card for either player.
Celtic, the 1967 European Cup winners who last reached the Champions League first knockout round in 2008, ran out of steam after the break but Ambrose spurned a chance to redeem himself by heading straight at Buffon when free.
Slightly out of the blue, Italy midfielder Marchisio then struck after being set up by Matri and Montenegro forward Vucinic made it three in style as Celtic, and especially Ambrose, hit a wall of fatigue.
