The Merseyside outfit lost to the Russian outfit last week, and need to score three goals in order to move on from the round of 32.
"The atmosphere will be really good and if we score early then our confidence will grow," Enrique told the club's official website. "It will be the biggest European game I've ever played in. We have really good players and I think we can score a lot of goals.
"The problem this season has been conceding goals. It's so important to keep a clean sheet against Zenit. They spent a lot of money so they have good players but we have to stop them scoring. We need to concentrate throughout."
Liverpool head into the fixture at Anfield on the back of a 5-0 win over Swansea City in the Premier League on Sunday.