Steed Malbranque also saw a powerful shot kept out by the Chornomorets goalkeeper, who had to be at his best to deny the former Fulham man.
The home side began to show their attacking side as the match progressed, but Aleksey Antonov fired over and then hit a shot at Remi Vercoutre. Ivan Bobko also found an opening, although his effort was blocked by a strong Lyon defence.
With half time approaching, Vercoutre was once again needed to prevent Antonov, who had worked space for the shot.
The second half started in a similar fashion to the first, with both sides having decent chances to open the scoring. Bobko missed the target for the hosts, while Malbranque thought he had scored with a left-footed shot, but Past made a good save.