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 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."
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."
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- Sergei Semak