The 16-year-old Cherki scored twice, provided two assists and won a penalty -- missed by Moussa Dembele -- in an eye-catching display as Lyon held off Nantes in the round of 32 on Saturday.
Lyon boss Rudi Garcia, who handed Cherki his professional debut against Dijon in October, said it was the youngster's all-round commitment that most pleased him.
"We know he's a boy who has the ability to decide a match. Of course that pleased me," said Garcia.
"What delighted me though was his overall game and how he played with his team-mates, the intelligence of his choices and his defensive runs. If he continues likes that he will be able to keep making progress."
Garcia must also try and temper expectations for a burgeoning talent who has drawn comparisons to fellow Lyon academy graduates Karim Benzema and Hatem Ben Arfa.
"My role is also to lower those levels because everyone is going to praise him to the skies, but he's only 16 years old," said Garcia.
"It's going to be a great danger if he stops listening to me, no longer works hard and thinks he's already made it, when he's still got a long way to go."
Nantes counterpart Gourcuff admitted he didn't know too much about Cherki but was quickly impressed by his breakout performance.
"He has a big future. He's a very, very good footballer," Gourcuff said succinctly.
It was only Cherki's eighth appearance for Lyon, and just a second start, but one that could prompt Garcia to fast-track his path to the first team, with Memphis Depay and Jeff Reine-Adelaide long-term absentees.
"We see him at training. Perhaps he surprised you but not us," said Lyon goalkeeper Anthony Lopes.
Cherki, who became the club's youngest goalscorer the previous round in a 7-0 rout of Bourg-en-Bresse, was quick to deflect to the acclaim.
"It's thanks to my team-mates that I had this kind of match," he said.
"You can't just dwell on the statistics, it's the whole team. Now we need to take care of the fixtures to come."
Lyon host Lille in the French League Cup semi-finals in midweek before welcoming bottom side Toulouse on January 26, when Cherki could make his first Ligue 1 start.