The veteran defender, making his 150th - and now last - European appearance, gifted Zenit's star forward Hulk a goal that gave the Russians a 3-0 aggregate lead early in the second leg of the last-32 tie.
Liverpool responded as top scorer Luis Suarez fired in two free-kicks and Joe Allen struck from close range but Hulk's vital away goal prevented another memorable Anfield fightback.
Liverpool's history is littered with stirring tales of European recoveries and the crowd longed for another to breathe new life into an inconsistent season.
The hosts went into the game with plenty of noise behind them and they looked determined to feed the atmosphere with the goals they required.
Brendan Rodgers' men were positive from the outset with Suarez, once again the main attacking focal point in the absence of the ineligible Daniel Sturridge, looking lively.
Suarez attempted to get behind the defence at every opportunity and almost got in on goal from a Jose Enrique long ball but he could not control.
Jordan Henderson won possession on the left but shot straight at Vyacheslav Malafeev from distance and Steven Gerrard lined up a free-kick only to blaze over.
Yet Zenit had no intention of sitting back on their advantage and there was a warning for Liverpool as Danny broke through and Carragher came across to block his run.
Carragher also made another timely interception but the Liverpool veteran had nowhere to hide after the 19th-minute blunder which gifted Zenit the opener.
The 35-year-old was under little pressure when he miscontrolled a speculative pass into the Liverpool half but Hulk quickly seized on the ball.
The £32million Brazilian, who scored in the first leg, raced through on goal and fired past Jose Reina with conviction.
The away goal left Liverpool needing to score four times to salvage the tie and they needed a quick response.
They got it as Daniel Agger burst forward from deep and was felled on the edge of the area by Nicolas Lombaerts.
Zenit sensed the danger and their best to delay the free-kick. Referee Bjorn Kuipers eventually tired of their capers and booked Igor Denisov and Suarez made them pay further by blasting the set-piece through the wall and into the net.
The crowd were reignited and Gerrard won another free-kick in dangerous territory moments later but Aleksandr Anyukov headed the captain's set-piece behind.
Hearts were in mouths when Reina miskicked with Hulk again threatening but the goalkeeper recovered and Liverpool tried to build again.
There were further scares when Danny chested down a Hulk cross and volleyed narrowly wide and Anyukov also hit the side-netting but the Reds grabbed another before the break.
Enrique found space down the left and exchanged passes with Henderson before crossing from the byline for Allen.
Allen's initial header was parried by Malafeev but the Wales midfielder followed up to hook home.
Liverpool carried the momentum into the second half and had a strong appeal for a penalty turned down when Tomas Hubocan appeared to handle after Suarez won a header.
Suarez played on and blasted narrowly wide but Liverpool made their feelings clear to Kuipers soon enough.
It did not dent their enthusiasm and Zenit found it increasingly difficult to hold the Merseysiders back.
The next breakthrough came just before the hour after Suarez was fouled by Roman Shirokov outside the box.
Suarez and Gerrard stood behind the free-kick but it was the Uruguayan who again stepped up, curling an inch-perfect shot into the top corner.
That increased the noise level yet further but there was another warning for Liverpool when Hulk flashed a free-kick wide after substitute Jonjo Shelvey was booked for a crude challenge.
Another substitute, Oussama Assaidi, made a more positive contribution before being pulled back on the edge of the area.
Suarez fancied a hat-trick of free-kicks but his effort was beaten away by Malafeev.
Gerrard produced an acrobatic effort to get a shot on target from an awkward bouncing ball but Malafeev, who had pushed the ball in his direction, recovered to save again.
At the other end Reina saved well from Hulk and Liverpool attacked again with Shelvey firing wide.
Liverpool kept up the pressure until the end, with Reina going forward for a late corner, but it was not to be and Zenit will now face Swiss side Basle in the next round.