The Reds hopes of making the last 16 of the competition were dealt a major blow when Brazilian forward Hulk and Sergei Samek struck within minutes of each other to leave the Anfield outfit a large deficit to overcome in a week's time.
Steven Gerrard is 15/8 to score anytime against Swansea with bet365
The loss comes in the aftermath of defeat against West Brom, and Gerrard is now looking towards the weekend game against high-flying Swansea as a chance to right recent wrongs.
"We're obviously down. On the back of two defeats, it's a difficult moment but we need a reaction," he told the club's official website.
"We've got a big game in a couple of days against Swansea and we need to bounce back.
"Up until the 70th minute agains Zenit, the game was under control. It as a tough night in tough conditions. We're disappointed with the two sloppy goals we conceded, but the tie is not over. If anyone can pull it back, it's us."
Liverpool have been involved in many European comeback over the years - most famously against AC Milan in the 2005 Champions League final - and Gerrard hopes the fans will play a major part when Zenit travel to Merseyside for the second leg.
"We'll have an advantage with our supporters," he added.
"If they can create the noise they're capable of, get behind the team and we can get an early goal, it's game on.
"But we are disappointed. It wasn't the result we wanted - we wanted an away goal and to try and sneak away with a clean sheet, but if you concede sloppy goal, you get punished and that's what happened."