Having missed a number of chances - with top scorer Luis Suarez being the main culprit - the Reds went behind to Hulk's brilliant long-range effort after 70 minutes with substitute Sergei Semak adding the second moments later.
It leaves Liverpool's hopes of progress in the balance in the second-round return leg next week - but Rodgers remains optimistic.
"There is no way the tie is over, not by a long shot. We are more than capable of getting the goals back," he said.
"I think the next goal is vitally important for us and what gives us hope is we created enough to win the game.
"If we get it early it can create the momentum for us."
The manager defended his decision to take off Raheem Sterling late on and send on defensive midfielder Lucas Leiva instead of pushing for what would have been a decisive away goal.
"I was just making sure we stayed in the tie, that was the important thing for us.
"As much as we wanted to go on there is another game and at 2-0 you can retrieve something, at 3-0 it would have cost us.
"The idea was to try to secure the game and keep it where it was at knowing that is retrievable and gives us a fighting chance."
Rodgers was disappointed that, having created so many good chances and managed to keep Zenit at bay, they conceded the goals they did.
"It is one of those games where, after that first five or 10-minute spell, I thought we looked solid and a threat going forward and we could have been leading at half-time," he said.
"Going into the last 20-25 minutes I was thinking we could win the game but we gave away two poor goals.
"The first one is a terrific strike but we are disappointed with the build-up and we could have defended it better.
"We ended up losing the game when we probably should have won the game."
Rodgers refused to criticise Suarez - but the Uruguay international could have netted a first-half hat-trick.
"He could have had a hat-trick by half-time," Rodgers said. "It just wasn't his night but he's been brilliant for us all season.
"The important thing is that after his first one-on-one, he kept going and was still in there."
Although there was an unconfirmed report of one instance of a monkey chant being made the match passed off without incident despite fears that Zenit's racist element would target Liverpool's black players.
"I read and heard a lot about Zenit St Petersburg as a club, city and people before we got here," said Rodgers.
"I can only thank the club for how we've been received here.
"It has been fantastic - there were no problems at the game, it was a wonderful atmosphere and we want to thank the people of Zenit and Russia."
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