After a crushing win over Swansea, Liverpool returned to European duties by hosting Zenit hoping to overturn a 2-0 deficit from the away leg.
Liverpool started brightly with the Anfield faithful willing them on as Gerrard and Henderson had early openings.
The bright start suffered a massive blow in the 19th minute as Carragher (making his 150th European appearance) miss-hit a back pass which was intercepted by Hulk who went one-on-one with Reina and slotted home to open the scoring and put Zenit 3-0 up on agg meaning Liverpool needed four goals without reply to go through to the next stage.
Liverpool still had hope and soon equalised after Agger's run through the defence saw him fouled and Suarez swept in a superb free kick which bypassed the wall and keeper to send Anfield into an erupting roar.
A quick second was denied on the line by Anyukov after Gerrard's effort but the comeback was complete two minutes before the interval as a great exchange between Henderson and Enrique created space for the Spaniard to cross. The cross found Allen who was initially denied by Malafeev but then lifted the ball over the keeper to hand Liverpool a 2-1 lead on the night.
The second half saw an early shout for a penalty after a Hubocan handball but the referee waved play on with Suarez then firing wide as the home crowd protested.
Suarez has been a hero for Liverpool all season and continued the form in 59th minute by stepping up to a free-kick from 30 yards out and bending it home past Malafeev to level the tie and put Liverpool 3-1 up, but due to the away goals rule another goal was needed.
The performance was proving to be another historic European night at Anfield as Suarez looked to complete a hat-trick of free-kicks but this time he was denied by Malafeev and the keeper also acrobatically stopped a strong volley from Gerrard.
The clock was ticking on and Shelvey went close only to hit the side netting and an Agger header skimmed wide before the final whistle went and meant an exit for Liverpool from the competition.
A sad way for Carragher to mark what was his 150th but also his last appearance in European competition with a mistake that led to the goal which kept the advantage for Zenit and left Liverpool with mixed emotions, sad after bowing out on away goals but with positives in securing a 3-1 win which saw them dominate their opponents.
Due to the Swansea game being brought forward, Liverpool's next game is in March against Wigan in a game many will be cautious about given that last season the Latics caused a surprise win which aided a run to surviving relegation so lightning could strike twice.