The Rossoneri are in Russia for their second Group C game at Stadion Petrovski, and Allegri admits that bagging maximum points will not be easy.
"This will be an important contest because it is between the two group favourites, neither of whom played to their potential in the first round of games," he said. "I have watched many of Zenit's matches and I don't think you can say they are a team in crisis.
"[Luciano] Spalletti is an excellent and clever coach. His task is to ensure that all the players in this game have forgotten about any other problems.
"Russian football is continuing to evolve and we are seeing that good players from all over the world are going to Russia."
However, Allegri is determined not to let Zenit have it easy on their home turf.
"Maybe my players do not have the same levels of understanding as Zenit's, but we are in good shape," said the Italian.
"Technically we are very strong and we have shown improvement in recent matches. On Wednesday we are ready to play even better."
In the other Group C game on Wednesday, Anderlecht will host Malaga.