Son Heung-min's brace was enough for the visitors to seal three points at at the Stadion Petrovsky, despite Jose Rondon's late consolation goal in the Group C clash.
The win leaves Zenit with plenty of work to do if they are to qualify for the knockout stages after falling to a second defeat against Leverkusen despite dominating the early stages.
In third place on four points going into clashes with Benfica and Monaco, Villas-Boas was satisfied with his side's endeavour.
"We were very unlucky because we were very good overall, unfortunately we couldn't take all of our chances, which meant that when we took our chances already it was 2-0," he explained.
"It was too late, but the players were fantastic - the emotions, the intensity were all great. The first half was very good, we passed the ball very well, Aleksandr Kerzhakov had two good chances so I think that we deserved to be leading in the first half.
"In the second it was about the same, but Leverkusen had their chances and they scored. They scored on a wonderful set-play and then they scored on the counter attack to make it 2-0.
"But we congratulate Leverkusen, they played wonderfully and were fantastic in defence, but I think that the final result is unfair."
The former Chelsea and Tottenham boss was certain, however, that the remaining two group games are must-win clashes for his side.
"Our chances depend a little bit on what happens with Benfica and Monaco, of course it would be important for Benfica to win or Monaco to draw for us to have a good chance," he added.
"What doesn't change is our responsibility to win the last two games."
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
