Luciano Spalletti's men still hold top spot in the Russian Premier League but only by a narrow margin now after taking just one point from their last three matches.
Zenit's loss of form goes beyond the league as well, with the 2012 Russian champions now without a win in their last five games in all competitions - having previously won seven of eight.
That is not the sort of form Zenit would have been hoping for going into their clash with Diego Simeone's red-hot Atletico, but they are looking for better on Tuesday night.
Midfielder Oleg Shatov said on his club's website: "I don't think there's any downturn or crisis in the team. I think that we've showed good football in many games, even when we lost.
"Nobody likes to lose, especially us. We have all the cards we need to rectify the situation."
Atletico have already assured themselves of top spot in Group G after winning all of their opening four matches, but Zenit could possibly secure runners-up spot with a win this week if third-placed Porto slip up against Austria Vienna.
Simeone has opted to rest a number of his key players for the trip to Russia, including Diego Costa, David Villa, Arda Turan, Tiago and Filipe Luis, but even facing a weakened Atletico side, Shatov is refusing to make any predication about Tuesday's result.
"I can't make any promises. This is football and anything can happen," he said.
"But I can say for myself and for the team that we have nowhere to retreat to. We need to win, we will play to win, and we'll try to please our fans at the end of the match."
He added: "Atletico have been surprising everyone this season. They're in second place in Spain and they've already advanced in the Champions League. Simeone has created a strong team."
Zenit will be without Danny and Cristian Ansaldi for the match while Aleksandr Anyukov faces a late fitness test.
Atletico make the trip to Russia in stunning form, with Saturday's 7-0 derby mauling of Getafe making it 16 wins in 20 competitive matches this season - with just the one defeat.
The Rojiblancos will aim to continue that run at the Petrovski Stadium, although defender Toby Alderweireld is not expecting it to be easy.
"The Zenit game is going to be tough. They have to win and it's a long trip, but I think we can do well," said the Belgium international on his club's website.