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."
"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.
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.
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.
