Zenit opened the scoring just before half-time, when Sardar Azmoun prodded home following a clever interchange on the edge of the penalty area.
Lyon did level just after the break thanks to a Memphis Depay penalty, but it ultimately felt like a missed opportunity for the Ligue 1 side, as they dropped points at home in their Group G opener.
Sylvinho – who was taking charge of a Champions League game for the first time – believes Lyon's start to the game left them with an uphill task, even if Zenit did not break the deadlock until the 41st minute.
"We started badly, maybe because we were a bit stressed," the Brazilian told reporters. "We then pulled ourselves together and had more of the possession before conceding the goal that destabilised us.
"We could have won given the way the game went after that. I have a young team that needs support from everybody, from the fans and the coaching staff."
Lyon midfielder Lucas Tousart put the hosts' woes down to a lack of creative ingenuity.
"We conceded the goal and then in an attacking sense we weren't dangerous enough in the final third in order to be able to score," he added.
"They sat very deep and we lacked creativity and inspiration. We lacked a killer touch in certain situations."
Zenit coach Sergei Semak was convinced a draw reflected the pattern of play, though he also felt the visitors could have taken the spoils.
"I think the result is fair," he said. "Lyon did put us under pressure but a number of goalscoring opportunities from both sides were probably equal. It's a tough group and anything is possible here."