Villas-Boas' men sunk without a trace at the BayArena on Wednesday, Giulio Donati and Kyriakos Papadopoulos securing all three points for the German side.
Brazilian defender Wendell's sending off with 11 minutes remaining offered some hope, yet Zenit could not find a way through.
The result leaves Villas-Boas' men third in the group ahead of the reverse fixture in two weeks, although they are just two points adrift of leaders Leverkusen.
"The group is developing exactly as we expected," he told the club's official website.
"It is still possible, and in the second leg, we must do everything to come back and continue the struggle for qualification."
Zenit's next encounter will be a difficult task, though, versus a Leverkusen side that impressed Villas-Boas.
He added: "We must pay tribute to Bayer, who attacked more and deprived us of the ball."
