"There's a lot of emotion, joy, pride and relief as it was difficult," Lyon coach Bruno Genesio told RMC Sport. "We deserved the result and qualification. I'm very proud of the players because we came here to play and didn't come away from home to play for a draw."
Genesio had come under fire for including Fekir in the starting line-up in Kiev following a series of poor outings.
But his goal capped off a dynamic performance at the heart of the Lyon midfield. "I'm really pleased that Nabil scored the goal as people have been questioning him of late," added Genesio.
Lyon, who finished as runners-up in Group F behind Manchester City, will go into Monday's draw for the knockout stages to face pool winners such Juventus, Barcelona, Bayern Munich and Real Madrid.
They will not be pitted against the Group C winners Paris Saint-Germain as they are both from the same country.
"We did everything we could to keep hold of the lead but we couldn't do it," said Shakhtar coach Paulo Fonseca. "The individual quality of Fekir made the difference."