The Northern Irishman believes the Reds can still qualify for the last 16 but conceded that his side gave "two poor goals away" and stressed the need to be "more clinical"
The Northern Irishman could only watch anxiously as second half strikes from Hulk and Sergey Semak condemned the Reds to their second defeat on Russian soil this season.
But Rodgers believes the deficit is "retrievable" - especially if Liverpool can score first in the second leg, while he also thinks his side's overall performance was good enough to earn them victory in St Petersburg.
"[2-0] is retrievable and gives us a fighting chance," Rodgers told reporters. "The next goal will be vitally important in the tie and if we can get it, it will give us momentum.
"I thought we looked solid and a threat going forward and could have been in the lead at half-time.
"But we gave away two poor goals tonight. We ended up losing the game when we should have won it."
Amid pre-match fears of racist supporters, Rodgers was also keen to thank those in St Petersburg for their welcoming hospitality, but he did state the need for his side to be more clinical.
"I want to thank the people of St Petersburg for their hospitality and how we've been received here.
"In 6 to 12 months' time, we won't be making those mistakes. This is part of our growing pains as a group. We have to be more clinical."