Trailing 2-0 from the first leg, the Reds looked doomed after Hulk’s early goal made the aggregate score 3-0. However, Liverpool rallied and two free-kicks from Luis Suarez plus another strike from Joe Allen, brought the scores to 3-3 although Zenit held on to advance on away goals.
Despite exiting the competition, Rodgers had few complaints about his team’s display.
“I thought we were incredible,” said the Irishman.
“At 3-0 you might have thought the tie was over and done with. But we showed real character and quality tonight to get three goals, and we totally dominated the game, controlled the game and should have had a penalty. We’re bitterly disappointed and lost the battle tonight, but in terms of the war going forward we very much look forward to that.”
Jamie Carragher, making his 150th European appearance had nowhere to hide after his 19th-minute blunder 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 and fired past Jose Reina.
The away goal left Liverpool needing to score four times to salvage the tie and they needed a quick response.
And they made a good fist of it when first Suarez blasted a free-kick through the wall and into the net before Allen netted soon after to give them hope.
They got their third just before the hour when the Uruguayan curled an inch-perfect shot into the top corner.
It looked like one of the great Anfield comebacks was on the cards and Suarez fancied a hat-trick of free-kicks but his next effort was beaten away by Malafeev.
Liverpool kept up the pressure, with Reina going forward for a late corner, but it was not to be.
LIVERPOOL: Reina, Johnson, Carragher, Agger, Jose Enrique, Lucas, Allen (Shelvey 59), Downing (Sterling 84), Gerrard, Henderson (Assaidi 59), Suarez.
ZENIT ST PETERSBURG: Malafeev, Aniukov, Luis Neto, Lombaerts (Criscito 46), Hubocan, Witsel, Denisov, Shirokov, Danny (Faitzulin 46), Hulk, Semak (Rodic 84).
Ref: Bjorn Kuipers (Holland).