The Serie A giants looked dead and buried after goals by Sami Hyypia and Luis Garcia gave Liverpool a commanding 2-0 half-time lead.
However, Juventus are favourites to qualify for the semi-finals after Carson allowed Fabio Cannavaro to score as the first leg finished 2-1.
Benitez, however, insists Liverpool have the character to grind out a result at the Stadio Delle Alpi on April 13 and advance to the last four.
“I don’t think it was an error by Scott,” said Benitez afterwards.
“The ball bounced right in front of him and it was difficult.
The goal deprived Liverpool of a two-goal cushion to take to Juventus, whose famed defence was startlingly undermined by the pace and imagination displayed by Liverpool before they faded in the second-half.
Captain Steve Gerrard said: “Scott will be disappointed with the goal he conceded but his first half save from Alessandro Del Piero was as good as I have seen.”
Memories of that tragic night at the Heysel Stadium in Brussels twenty years ago had dominated the build-up and the tone was epitomised by the Italian word ‘Amicizia’ - friendship - and Fabio Capello, the Juventus coach who predicted there would be a wonderful atmosphere, was not disappointed.
The minute’s silence before kick-off was organised to mark the death of Pope John Paul II, but had extra significance for so many from Merseyside and Turin. It coincided with supporters in the Kop brandishing cards that spelled out a message of friendship between the two clubs and prompted applause from Juventus supporters.
The air of reconciliation thankfully did not dissolve, but the optimism of those Juve fans quickly diminished. They are not accustomed to watching their team concede goals, but that happened after only 10 minutes as Liverpool were rewarded for starting the match at a high tempo that clearly disturbed the Italians.
If Juventus’s early sign of fallibility was unexpected, the man who exposed them was equally surprising. Sami Hyypia was playing his first game for a month, but showed a marvellous striker’s instinct when he volleyed past Gianluigi Buffon after a corner was touched on.
Hyypia’s goal was the first conceded by Juventus in more than a month, but they had looked uncomfortable from the opening seconds when Emerson’s slip allowed Baros shoot wide.
The Liverpool manager Rafael Benitez could not have envisaged such a magnificent opening to the quarter-final, but he deserved such a response after taking a risk in his selection.
Benitez, deprived of all his strikers apart from Milan Baros because of injuries, surprised the Liverpool supporters by choosing Carson in goal ahead of Jerzy Dudek, while Antony Le Tallec was a surprise selection as he started his first game for a year in midfield. Both were to justify Benitez’s belief in them long before half-time, although 19-year-old Carson was at fault later in the game.
Le Tallec’s best moment came in the 19th minute when, wide on the right, he played in a pass that bounced perfectly for Luis Garcia to volley past Juventus’s Buffon, a £32m keeper who is unaccustomed to conceding one goal in a game, never mind two. Anfield has witnessed many memorable European nights; it has seen few finer European goals.
Jamie Carragher and Steven Gerrard also went close in the first-half powering in excellent off-target efforts during an opening half when similar threats from Juventus were rare. Pavel Nedved, rarely involved before the break, directed a shot wide in the 26th minute.
But the shell-shocked Italians went closest to a first-half goal on the half-hour when Carson - not born at the time of the Heysel tragedy - justified Benitez’s faith by superbly turning away a shot from Alessandro Del Piero.
But Del Piero was also unfortunate when he lobbed the ball over Carson shortly before the interval. Carson would claim that he had spotted the flag that told Del Piero he was offside, while the Italian striker could argue with justification that the decision was harsh.
The disallowed goal represented the climax to a memorable opening half and it was quickly obvious there would not be similar drama for the remaining 45 minutes as Liverpool tempered their attacking instincts in an attempt to sustain a two-goal lead that would give them a crucial edge in the second leg.
It proved to be a dangerous strategy. The first 10 minutes brought a wayward shot from Nedved, while Del Piero had claims for a penalty rejected by the referee as Liverpool tried to rediscover their earlier pace and authority.
Nedved also fired a shot straight at Carson and a good intervention by Jamie Carragher rescued another awkward situation before a mistake by the keeper presented Juventus with an away goal that may prove influential in the final analysis.
With 63 minutes gone, defender Fabio Cannavaro pushed forward to meet a left-wing cross with a header that bounced awkwardly in front of Carson, who made a feeble attempt to push it away. It was an unwanted addition to the litany of goalkeeping errors in England this season and ensured that Liverpool were under intense pressure for the final third of a game that appeared to be in their grasp in its earlier stages.
Liverpool’s attacking threat had now disappeared and the withdrawal of Baros after 66 minutes signalled that they were content to hang on to their narrow advantage rather than risk losing it by chasing more goals.
Benitez’s team succeeded in that limited aim as the game drifted to a close, but Juventus - in danger of being swept away in the opening half-hour of the game - returned to Italy as marginal favourites to progress to the semi-finals when the teams meet at the Stadio Della Alpi next week.