Aurier provided the assists for both Wilfried Bony and Gervinho as Ivory Coast reversed a 1-0 deficit to beat Alberto Zaccheroni's side 2-1 in their FIFA World Cup opener on Saturday.
The 21-year-old Toulouse man was in superb form throughout the Group C contest in Recife, and such performances are only likely to heighten the speculation over his future - with Premier League giants Arsenal reported to be interested in his services.
And Chelsea legend Drogba has no doubt that his countryman has the necessary quality to star in England's top flight.
"Serge brought us energy and balance, and he had a fantastic game," said the 36-year-old.
"He's the best right-back in all of France. I think he'll do well at the next level too, in the Premier League.
"It's good to see we have a new generation coming through.
"This is what we need and it's good for our football. It gives us energy. It gives us spirit.
"We're trying to bring all the young ones up the right way, to bring them along in the spirit of this team."
Ivory Coast face a crucial clash with Colombia - who beat Greece 3-0 in their first World Cup fixture - on Thursday, before ending their group campaign against Greece next week.