An Alexsandr Kerzhakov penalty earned the Russian club a narrow victory and Spalletti was keen to praise his team's performance following the match.
The Italian told Zenit's official website: "Of course we expected a difficult game today because of pressure from the fact that we had to win. The pitch was difficult, and our opponent was strong.
"We were aware that the game would not be a simple one. I think we played well most of all in terms of team balance. We attacked a lot without losing our balance.
"We played wisely today. I think we made a lot of scoring opportunities. From my point of view, we deserved to win today."
Zenit are currently third in Group C, behind AC Milan and Malaga.