The point gives the Russian side a chance of progressing to the last 16 of the competition going into the final match of Group G.
After going behind to a Adrian Lopez strike early in the second half, Zenit fought hard and drew level fortuitously when Igor Smolnikov's right-wing cross deflected off the head of Toby Alderweireld and looped over Thibaut Courtois in the 74th minute.
Spalletti was delighted to have snatched a point, adding that he was pleased to see their dominance in possession rewarded.
"We had dangerous runs in behind their defenders," the Italian said. "We played a passing game and we tried to attack in different ways.
"I'm happy that my team played football. Some things did not work out, but we played like we had to."
Zenit face Austria Vienna in their final group match as they look to reach the knockout stages for only the second time.
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