Allegri believes his team have it all to do if they are to come away with the three points.
"We have to prove to be a good team on a technical level," he said. "But we still have a lot to improve on. Zenit are a very good team.
"Russian football has evolved greatly. The arrivals of Hulk and Axel Witsel has seen them make a great leap forward.
"[Zenit boss] Luciano Spalletti is an excellent Coach. He won the Coppa Italia with Roma, and has won the League here in Russia. His teams always play good football."