The Russian club took a big step towards a fourth straight appearance in the Champions League group stages thanks to Oleg Shatov's away goal in Belgium.
However, despite impressive early-season form that has seen Zenit win all four of their league games, scoring 15 goals in the process, coach Villas-Boas has urged his side to guard against complacency ahead of next week's second leg in St Petersburg.
"Our job is not finished yet and I suppose the return match will be just as difficult as the one today," said the Portuguese.
"But that is a normal thing considering the level of this Champions League competition.
"Overall it was a good performance from my team.
"Of course we played better in the first half than we did in the second. We lost too much ball in possession after half-time and Standard used crosses and set-piece situations from which they then created opportunities.
"But I want to underline that I am pleased with our overall performance in this match.
"It is a pity we could not score a second goal as that would have made our job easier for the second leg back home."
