The Reds entered the second leg of the tie at Anfield 2-0 behind their Russian rivals.
This lead was quickly extended, as Brazilian striker Hulk pounced on a Jamie Carragher mistake to slot home.
However, the Reds fought back to win 3-1 on the night thanks to a Luis Suarez double and a close range effort from Joe Allen.
However, they were unable to find the all-important fourth, meaning Zenit advanced via away goals with the aggregate score 3-3.
Rodgers was happy with his team’s efforts across both legs, and felt that they showed great spirit to battle back despite their disadvantage:
“I thought we were incredible,” he is quoted by Sky Sports.
“Obviously we were two down from the first leg and to concede again, 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 very proud of the club and the players tonight. They showed why they’re part of the world’s best football family.”
Rodgers went on to say that he is happy with the progress his team are making, and insisted that they are heading in the right direction:
“We’re bitterly disappointed and we lost the battle tonight, but in terms of the war going forward we very much look forward to that. Overall we were fantastic.”